A036378 matched A095005+A095006 in 33 positions.
A036378 matched A095007+A095008 in 33 positions.
A036378 matched A095013+A095014 in 33 positions.
A036378[1] != (A095015[1]+A095016[1]), i.e. 1 != (0+0)
A036378 matched A095015+A095016 in 32 positions.
A036378 matched A095019+A095054 in 33 positions.
A036378 matched A095020+A095055 in 33 positions.
A095013 matched A095009+A095012 in 33 positions.
A095014 matched A095010+A095011 in 33 positions.
A095054 matched A095018+A095020 in 33 positions.
A095055 matched A095018+A095019 in 33 positions.
A036378 matched A095063+A095064 in 33 positions.
A036378 matched A095060+A095061 in 33 positions.
A095060 matched A095062+A095067 in 33 positions.
A095061 matched A095066+A095069 in 33 positions.
A095062 matched A095065+A095068 in 33 positions.
A095008[3] != (A095092[3]+A095093[3]), i.e. 1 != (0+0)
A095008[4] != (A095092[4]+A095093[4]), i.e. 3 != (0+0)
A095008[5] != (A095092[5]+A095093[5]), i.e. 3 != (0+0)
A095008[6] != (A095092[6]+A095093[6]), i.e. 7 != (0+0)
A095008[7] != (A095092[7]+A095093[7]), i.e. 13 != (0+0)
A095008[8] != (A095092[8]+A095093[8]), i.e. 22 != (0+0)
A095008[9] != (A095092[9]+A095093[9]), i.e. 37 != (0+0)
A095008[10] != (A095092[10]+A095093[10]), i.e. 71 != (0+0)
A095008[11] != (A095092[11]+A095093[11]), i.e. 128 != (0+0)
A095008[12] != (A095092[12]+A095093[12]), i.e. 231 != (0+0)
A095008[13] != (A095092[13]+A095093[13]), i.e. 440 != (0+0)
A095008[14] != (A095092[14]+A095093[14]), i.e. 807 != (0+0)
A095008[15] != (A095092[15]+A095093[15]), i.e. 1519 != (0+0)
A095008[16] != (A095092[16]+A095093[16]), i.e. 2872 != (0+0)
A095008[17] != (A095092[17]+A095093[17]), i.e. 5371 != (0+0)
A095008[18] != (A095092[18]+A095093[18]), i.e. 10204 != (0+0)
A095008[19] != (A095092[19]+A095093[19]), i.e. 19341 != (0+0)
A095008[20] != (A095092[20]+A095093[20]), i.e. 36759 != (0+0)
A095008[21] != (A095092[21]+A095093[21]), i.e. 70179 != (0+0)
A095008[22] != (A095092[22]+A095093[22]), i.e. 134241 != (0+0)
A095008[23] != (A095092[23]+A095093[23]), i.e. 256856 != (0+0)
A095008[24] != (A095092[24]+A095093[24]), i.e. 492936 != (0+0)
A095008[25] != (A095092[25]+A095093[25]), i.e. 947272 != (0+0)
A095008[26] != (A095092[26]+A095093[26]), i.e. 1822615 != (0+0)
A095008[27] != (A095092[27]+A095093[27]), i.e. 3513691 != (0+0)
A095008[28] != (A095092[28]+A095093[28]), i.e. 6781495 != (0+0)
A095008[29] != (A095092[29]+A095093[29]), i.e. 13103816 != (0+0)
A095008[30] != (A095092[30]+A095093[30]), i.e. 25348667 != (0+0)
A095008[31] != (A095092[31]+A095093[31]), i.e. 49092241 != (0+0)
A095008[32] != (A095092[32]+A095093[32]), i.e. 95168205 != (0+0)
A095008[33] != (A095092[33]+A095093[33]), i.e. 184661253 != (0+0)
A095008 matched A095092+A095093 in 2 positions.
A036378[3] != (A095094[3]+A095095[3]), i.e. 2 != (0+0)
A036378[4] != (A095094[4]+A095095[4]), i.e. 5 != (0+0)
A036378[5] != (A095094[5]+A095095[5]), i.e. 7 != (0+0)
A036378[6] != (A095094[6]+A095095[6]), i.e. 13 != (0+0)
A036378[7] != (A095094[7]+A095095[7]), i.e. 23 != (0+0)
A036378[8] != (A095094[8]+A095095[8]), i.e. 43 != (0+0)
A036378[9] != (A095094[9]+A095095[9]), i.e. 75 != (0+0)
A036378[10] != (A095094[10]+A095095[10]), i.e. 137 != (0+0)
A036378[11] != (A095094[11]+A095095[11]), i.e. 255 != (0+0)
A036378[12] != (A095094[12]+A095095[12]), i.e. 464 != (0+0)
A036378[13] != (A095094[13]+A095095[13]), i.e. 872 != (0+0)
A036378[14] != (A095094[14]+A095095[14]), i.e. 1612 != (0+0)
A036378[15] != (A095094[15]+A095095[15]), i.e. 3030 != (0+0)
A036378[16] != (A095094[16]+A095095[16]), i.e. 5709 != (0+0)
A036378[17] != (A095094[17]+A095095[17]), i.e. 10749 != (0+0)
A036378[18] != (A095094[18]+A095095[18]), i.e. 20390 != (0+0)
A036378[19] != (A095094[19]+A095095[19]), i.e. 38635 != (0+0)
A036378[20] != (A095094[20]+A095095[20]), i.e. 73586 != (0+0)
A036378[21] != (A095094[21]+A095095[21]), i.e. 140336 != (0+0)
A036378[22] != (A095094[22]+A095095[22]), i.e. 268216 != (0+0)
A036378[23] != (A095094[23]+A095095[23]), i.e. 513708 != (0+0)
A036378[24] != (A095094[24]+A095095[24]), i.e. 985818 != (0+0)
A036378[25] != (A095094[25]+A095095[25]), i.e. 1894120 != (0+0)
A036378[26] != (A095094[26]+A095095[26]), i.e. 3645744 != (0+0)
A036378[27] != (A095094[27]+A095095[27]), i.e. 7027290 != (0+0)
A036378[28] != (A095094[28]+A095095[28]), i.e. 13561907 != (0+0)
A036378[29] != (A095094[29]+A095095[29]), i.e. 26207278 != (0+0)
A036378[30] != (A095094[30]+A095095[30]), i.e. 50697537 != (0+0)
A036378[31] != (A095094[31]+A095095[31]), i.e. 98182656 != (0+0)
A036378[32] != (A095094[32]+A095095[32]), i.e. 190335585 != (0+0)
A036378[33] != (A095094[33]+A095095[33]), i.e. 369323305 != (0+0)
A036378 matched A095094+A095095 in 2 positions.
A036378 matched A095290+A095291 in 33 positions.
A036378 matched A095292+A095293 in 33 positions.
A036378 matched A095294+A095295 in 33 positions.
A036378 matched A095296+A095297 in 33 positions.
A036378 matched A095332+A095333 in 33 positions.
A036378 matched A095334+A095335 in 33 positions.
A036378 matched A095326+A095327 in 33 positions.
A036378 matched A095328+A095329 in 33 positions.
A036378 matched A095330+A095331 in 33 positions.
A036378 matched A095324+A095325 in 33 positions.
A036378 matched A095765+A095766 in 33 positions.
%I A000045
%S A000045 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,
%T A000045 10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,
%U A000045 1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169
%N A000045 Fibonacci numbers: F(n) = F(n-1) + F(n-2), F(0) = 0, F(1) = 1, F(2) = 1, ...
%Y A000045 HERE JUST FOR CHECKING!
%H A000045 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A000045 nonn
%O A000045 1,3
%A A000045 njas,
%I A003714
%S A003714 1,2,4,5,8,9,10,16,17,18,20,21,32,33,34,36,37,40,41,42,64,65,66,68,
%T A003714 69,72,73,74,80,81,82,84,85,128,129,130,132,133,136,137,138,144,145,
%U A003714 146,148,149,160,161,162,164,165,168,169,170,256,257,258,260,261
%N A003714 Fibbinary numbers
%Y A003714 HERE JUST FOR CHECKING!
%H A003714 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A003714 nonn
%O A003714 1,2
%A A003714 njas,
%I A037888
%S A037888 0,1,0,1,0,1,0,1,0,2,1,2,1,1,0,1,0,2,1,1,0,2,1,2,1,1,0,2,1,1,0,1,
%T A037888 0,2,1,2,1,3,2,2,1,3,2,1,0,2,1,2,1,1,0,3,2,2,1,3,2,2,1,2,1,1,0,1,
%U A037888 0,2,1,2,1,3,2,1,0,2,1,2,1,3,2,2,1,3,2,1,0,2,1,2,1,3,2,1,0,2,1,2
%N A037888 Binary asymmetricity-index
%Y A037888 HERE JUST FOR CHECKING!
%H A037888 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A037888 nonn
%O A037888 1,10
%A A037888 Clark Kimberling (ck6(AT)evansville.edu),
%I A036378
%S A036378 1,2,2,5,7,13,23,43,75,137,255,464,872,1612,3030,5709,10749,20390,
%T A036378 38635,73586,140336,268216,513708,985818,1894120,3645744,7027290,
%U A036378 13561907,26207278,50697537,98182656,190335585,369323305
%N A036378 Number of primes p such that 2^n < p < 2^(n+1).
%Y A036378 a(n) = A095005(n)+A095006(n) = A095007(n) + A095008(n) = A095013(n) + A095014(n) = A095015(n) + A095016(n) (for n > 1) = A095021(n)+A095022(n)+A095023(n)+A095024(n) = A095019(n)+A095054(n) = A095020(n)+A095055(n) = A095060(n)+A095061(n) = A095063(n)+A095064(n) = A095094(n)+A095095(n). Cf. A095354.
%H A036378 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A036378 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A036378 nonn
%O A036378 1,2
%A A036378 Labos E. (labos(AT)ana1.sote.hu), May 13 2004
%I A095005
%S A095005 0,1,2,2,5,8,19,20,48,75,160,242,505,835,1761,2799,5890,10250,20921,
%T A095005 36872,74316,134816,267749,492286,977207,1823657,3598657,6779899,
%U A095005 13336543,25358424,49763462,95140695,186504600
%N A095005 Number of odious primes (A027697) in range ]2^n,2^(n+1)].
%Y A095005 a(n) = A036378(n)-A095006(n).
%H A095005 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095005 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095005 nonn
%O A095005 1,3
%A A095005 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095006
%S A095006 1,1,0,3,2,5,4,23,27,62,95,222,367,777,1269,2910,4859,10140,17714,
%T A095006 36714,66020,133400,245959,493532,916913,1822087,3428633,6782008,
%U A095006 12870735,25339113,48419194,95194890,182818705
%N A095006 Number of evil primes (A027699) in range ]2^n,2^(n+1)].
%Y A095006 a(n) = A036378(n)-A095005(n).
%H A095006 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095006 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095006 nonn
%O A095006 1,4
%A A095006 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A027697
%S A027697 2,7,11,13,19,31,37,41,47,59,61,67,73,79,97,103,107,109,127,131,137,
%T A027697 151,157,167,173,179,181,191,193,199,211,223,227,229,233,239,241,
%U A027697 251,271,283,307,313,331,367,379,397,409,419,421,431,433,439,443
%N A027697 Odious primes: primes with odd number of 1's in binary expansion.
%Y A027697 Complement of A027699 in A000040. Union of A091206{3} and odious members of A091209. Cf. A095005.
%H A027697 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A027697 nonn
%O A027697 1,1
%A A027697 njas,
%I A027699
%S A027699 3,5,17,23,29,43,53,71,83,89,101,113,139,149,163,197,257,263,269,
%T A027699 277,281,293,311,317,337,347,349,353,359,373,383,389,401,449,461,
%U A027699 467,479,503,509,523,547,571,593,599,619,643,673,683,691,739,751
%N A027699 Evil primes: primes with even number of 1's in binary expansion.
%Y A027699 Complement of A027697 in A000040. Cf. A095006.
%H A027699 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A027699 nonn
%O A027699 1,1
%A A027699 njas,
%I A095007
%S A095007 0,1,1,2,4,6,10,21,38,66,127,233,432,805,1511,2837,5378,10186,19294,
%T A095007 36827,70157,133975,256852,492882,946848,1823129,3513599,6780412,
%U A095007 13103462,25348870,49090415,95167380,184662052
%N A095007 Number of 4k+1 primes (A002144) in range ]2^n,2^(n+1)].
%Y A095007 a(n) = A036378(n)-A095008(n) = A095009(n)+A095011(n).
%H A095007 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095007 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095007 nonn
%O A095007 1,4
%A A095007 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095008
%S A095008 1,1,1,3,3,7,13,22,37,71,128,231,440,807,1519,2872,5371,10204,19341,
%T A095008 36759,70179,134241,256856,492936,947272,1822615,3513691,6781495,
%U A095008 13103816,25348667,49092241,95168205,184661253
%N A095008 Number of 4k+3 primes (A002145) in range ]2^n,2^(n+1)].
%Y A095008 a(n) = A036378(n)-A095007(n) = A095010(n)+A095012(n) = A095092(n)+,A095093(n).
%H A095008 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095008 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095008 nonn
%O A095008 1,4
%A A095008 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095009
%S A095009 0,0,0,1,1,4,4,10,18,31,64,115,216,398,752,1413,2692,5092,9642,18355,
%T A095009 35089,66907,128431,246479,473201,911650,1756523,3390156,6551387,
%U A095009 12673576,24545135,47583812,92329094
%N A095009 Number of 8k+1 primes (A007519) in range ]2^n,2^(n+1)].
%Y A095009 a(n) = A095013(n)-A095012(n) = A095007(n)-A095011(n). Cf. A091126.
%H A095009 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095009 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095009 nonn
%O A095009 1,6
%A A095009 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095010
%S A095010 1,0,1,1,2,3,7,10,20,35,66,113,218,412,746,1460,2672,5104,9651,18375,
%T A095010 35105,67165,128410,246453,473535,911489,1756670,3390856,6552449,
%U A095010 12673142,24546849,47583904,92330578
%N A095010 Number of 8k+3 primes (A007520) in range ]2^n,2^(n+1)].
%Y A095010 a(n) = A095014(n)-A095011(n) = A095008(n)-A095012(n). Cf. A091127.
%H A095010 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095010 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095010 nonn
%O A095010 1,5
%A A095010 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095011
%S A095011 0,1,1,1,3,2,6,11,20,35,63,118,216,407,759,1424,2686,5094,9652,18472,
%T A095011 35068,67068,128421,246403,473647,911479,1757076,3390256,6552075,
%U A095011 12675294,24545280,47583568,92332958
%N A095011 Number of 8k+5 primes (A007521) in range ]2^n,2^(n+1)].
%Y A095011 a(n) = A095014(n)-A095010(n). Cf. A091128.
%H A095011 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095011 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095011 nonn
%O A095011 1,5
%A A095011 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095012
%S A095012 0,1,0,2,1,4,6,12,17,36,62,118,222,395,773,1412,2699,5100,9690,18384,
%T A095012 35074,67076,128446,246483,473737,911126,1757021,3390639,6551367,
%U A095012 12675525,24545392,47584301,92330675
%N A095012 Number of 8k+7 primes (A007522) in range ]2^n,2^(n+1)].
%Y A095012 a(n) = A095013(n)-A095009(n). Cf. A091129.
%H A095012 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095012 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095012 nonn
%O A095012 1,4
%A A095012 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095013
%S A095013 0,1,0,3,2,8,10,22,35,67,126,233,438,793,1525,2825,5391,10192,19332,
%T A095013 36739,70163,133983,256877,492962,946938,1822776,3513544,6780795,
%U A095013 13102754,25349101,49090527,95168113,184659769
%N A095013 Number of 8k+-1 primes (A001132) in range ]2^n,2^(n+1)].
%Y A095013 a(n) = A036378(n)-A095014(n) = A095009(n)+A095012(n).
%H A095013 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095013 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095013 nonn
%O A095013 1,4
%A A095013 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095014
%S A095014 1,1,2,2,5,5,13,21,40,70,129,231,434,819,1505,2884,5358,10198,19303,
%T A095014 36847,70173,134233,256831,492856,947182,1822968,3513746,6781112,
%U A095014 13104524,25348436,49092129,95167472,184663536
%N A095014 Number of 8k+-3 primes (A003629) in range ]2^n,2^(n+1)].
%Y A095014 a(n) = A036378(n)-A095013(n) = A095010(n)+A095011(n).
%H A095014 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095014 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095014 nonn
%O A095014 1,3
%A A095014 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095015
%S A095015 0,1,1,2,3,7,11,20,37,69,126,228,434,806,1514,2845,5361,10212,19308,
%T A095015 36747,70135,134065,256824,492871,946880,1822913,3513737,6780428,
%U A095015 13103565,25348226,49090715,95167496,184660541
%N A095015 Number of 6k+1 primes (A002476) in range ]2^n,2^(n+1)].
%Y A095015 a(n) = A036378(n)-A095016(n) (apart the initial term).
%H A095015 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095015 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095015 nonn
%O A095015 1,4
%A A095015 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095016
%S A095016 0,1,1,3,4,6,12,23,38,68,129,236,438,806,1516,2864,5388,10178,19327,
%T A095016 36839,70201,134151,256884,492947,947240,1822831,3513553,6781479,
%U A095016 13103713,25349311,49091941,95168089,184662764
%N A095016 Number of 6k+5 primes (A007528) in range ]2^n,2^(n+1)].
%Y A095016 a(n) = A036378(n)-A095015(n) (apart the initial term).
%H A095016 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095016 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095016 nonn
%O A095016 1,4
%A A095016 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095017
%S A095017 1,1,1,2,2,3,7,7,12,26,45,70,113,215,355,666,1153,2071,3785,6965,
%T A095017 12495,22643,41608,76371,140944,261752,484968,904799,1689477,3160113,
%U A095017 5928904,11139071,20970782
%N A095017 Number of lesser twin primes (A001359) in range ]2^n,2^(n+1)].
%Y A095017 Cf. A095016, A036378.
%H A095017 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095017 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095017 nonn
%O A095017 1,4
%A A095017 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095021
%S A095021 0,0,1,1,2,2,7,9,19,33,64,115,216,402,754,1434,2669,5116,9651,18382,
%T A095021 35064,67056,128394,246349,473469,911468,1757069,3389718,6551877,
%U A095021 12674065,24546590,47581820,92330910
%N A095021 Number of 5k+1 primes (A030430) in range ]2^n,2^(n+1)].
%Y A095021 Cf. A036378.
%H A095021 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095021 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095021 nonn
%O A095021 1,5
%A A095021 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095022
%S A095022 0,1,0,1,2,4,5,11,22,33,65,117,220,404,762,1422,2693,5123,9634,18409,
%T A095022 35112,67061,128302,246706,473477,911557,1756669,3390509,6552186,
%U A095022 12674857,24545491,47584387,92331524
%N A095022 Number of 5k+2 primes (A030432) in range ]2^n,2^(n+1)].
%Y A095022 Cf. A036378.
%H A095022 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095022 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095022 nonn
%O A095022 1,5
%A A095022 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095023
%S A095023 1,0,1,1,2,4,5,11,18,36,63,117,220,407,760,1435,2682,5074,9683,18392,
%T A095023 35113,67054,128503,246433,473717,911310,1756933,3390711,6551833,
%U A095023 12673497,24546404,47584981,92331321
%N A095023 Number of 5k+3 primes (A030431) in range ]2^n,2^(n+1)].
%Y A095023 Cf. A036378.
%H A095023 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095023 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095023 nonn
%O A095023 1,5
%A A095023 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095024
%S A095024 0,0,0,2,1,3,6,12,16,35,63,115,216,399,754,1418,2705,5077,9667,18403,
%T A095024 35047,67045,128509,246330,473457,911409,1756619,3390969,6551382,
%U A095024 12675118,24544171,47584397,92329550
%N A095024 Number of 5k+4 primes (A030433) in range ]2^n,2^(n+1)].
%Y A095024 Cf. A036378.
%H A095024 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095024 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095024 nonn
%O A095024 1,4
%A A095024 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095018
%S A095018 0,0,2,4,17,28,189,531,1990,5747,23902,76658,291478,982793,3677580,
%T A095018 13214719,49161612
%N A095018 Number of binarily balanced primes (A066196) in range ]2^(2n-1),2^2n].
%e A095018 Only primes in range ]2^5,2^6] with equal numbers of ones and zeros in their binary expansion are 37 (in binary 100101) and 41 (in binary 101011) thus a(3)=2.
%Y A095018 Cf. A095005-A095006, A095052-A095053.
%H A095018 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095018 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095018 nonn
%O A095018 1,3
%A A095018 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095052
%S A095052 0,1,3,10,25,78,283,906,3044,10920,37920,135182,487555,1764216,6415902,
%T A095052 23585285
%N A095052 Number of primes with number of 0-bits equal to one plus number of 1-bits (A095072) in range ]2^2n,2^(2n+1)].
%e A095052 In range ]2^4,2^5] 17 (10001 in binary) is only such prime thus a(2)=1.
%Y A095052 Cf. A095018.
%H A095052 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095052 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095052 nonn
%O A095052 1,3
%A A095052 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095053
%S A095053 1,1,5,11,28,105,362,1093,3659,13001,45171,159510,563833,2008295,
%T A095053 7333827,26730538
%N A095053 Number of primes with number of 1-bits equal to one plus number 0-bits (A095073) in range ]2^2n,2^(2n+1)].
%e A095053 In range ]2^2,2^3] 5 (101 in binary) is only such prime thus a(1)=1, and similarly, in range ]2^4,2^5] 19 (10011 in binary) is also unique in that respect, thus a(2)=1 as well.
%Y A095053 Cf. A095018.
%H A095053 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095053 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095053 nonn
%O A095053 1,3
%A A095053 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095056
%S A095056 0,1,2,1,2,3,3,0,4,2,3,2,2,2,4,1,3,4,5,3,2,1,5,1,0,2,5,2,2,8,6,0,
%T A095056 5
%N A095056 Number of primes with exactly three 1-bits (A081091) in range ]2^n,2^(n+1)].
%Y A095056 Cf. A095018.
%H A095056 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095056 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095056 nonn
%O A095056 1,3
%A A095056 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095057
%S A095057 0,0,0,2,2,5,4,10,6,13,11,9,16,16,18,25,15,19,15,37,17,37,29,29,32,
%T A095057 40,23,49,31,51,39,37,30
%N A095057 Number of primes with four 1-bits (A095077) in range ]2^n,2^(n+1)].
%Y A095057 Cf. A095018.
%H A095057 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095057 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095057 nonn
%O A095057 1,4
%A A095057 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095058
%S A095058 0,1,2,2,3,0,4,4,3,1,5,1,4,0,3,2,8,1,11,4,5,0,7,1,2,0,1,5,4,0,7,5,
%T A095058 1
%N A095058 Number of primes with a single 0-bit (A095078) in range ]2^n,2^(n+1)].
%Y A095058 Cf. A095018.
%H A095058 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095058 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095058 nonn
%O A095058 1,3
%A A095058 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095059
%S A095059 0,0,0,1,2,4,0,9,5,14,4,16,9,18,0,21,21,21,7,41,22,31,5,37,20,33,
%T A095059 14,37,45,47,0,69,31
%N A095059 Number of primes with two 0-bits (A095079) in range ]2^n,2^(n+1)].
%Y A095059 Cf. A095018.
%H A095059 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095059 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095059 nonn
%O A095059 1,5
%A A095059 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095072
%S A095072 17,67,73,97,263,269,277,281,293,337,353,389,401,449,1039,1051,1063,
%T A095072 1069,1109,1123,1129,1163,1171,1187,1193,1201,1249,1291,1301,1321,
%U A095072 1361,1543,1549,1571,1609,1667,1669,1697,1801,4127,4157,4211,4217
%N A095072 Primes in whose binary expansion the number of 0-bits is one more than the number of 1-bits.
%Y A095072 Intersect of A000040 & A031444. Subset of A095071. Cf. A095052.
%H A095072 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095072 nonn
%O A095072 1,1
%A A095072 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095073
%S A095073 5,19,71,83,89,101,113,271,283,307,313,331,397,409,419,421,433,457,
%T A095073 1103,1117,1181,1223,1229,1237,1303,1307,1319,1381,1427,1429,1433,
%U A095073 1481,1489,1559,1579,1607,1613,1619,1621,1637,1699,1733,1811,1861
%N A095073 Primes in whose binary expansion the number of 1-bits is one more than the number of 0-bits.
%Y A095073 Intersect of A000040 & A031448. Subset of A095070. Cf. A095053.
%H A095073 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095073 nonn
%O A095073 1,1
%A A095073 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095077
%S A095077 23,29,43,53,71,83,89,101,113,139,149,163,197,263,269,277,281,293,
%T A095077 337,353,389,401,449,523,547,593,643,673,773,1031,1049,1061,1091,
%U A095077 1093,1097,1217,1283,1289,1297,1409,1553,1601,2069,2083,2089,2129
%N A095077 Primes with exactly four 1-bits in their binary expansion.
%Y A095077 Subset of A027699. Differs from A085448 first time at n=19, where a(n)=337, while A085448 continues from there with 311, whose binary expansion has six 1-bits, not four. Cf. A095057.
%H A095077 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095077 nonn
%O A095077 1,1
%A A095077 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095078
%S A095078 2,5,11,13,23,29,47,59,61,191,223,239,251,383,479,503,509,991,1019,
%T A095078 1021,2039,3583,3967,4079,4091,4093,6143,15359,16127,16319,16381,
%U A095078 63487,65407,65519,129023,131063,245759,253951,261631,261887,262079
%N A095078 Primes with a single 0-bit in their binary expansion.
%Y A095078 Intersect of A000040 & A030130. Cf. A095058.
%H A095078 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095078 nonn
%O A095078 1,1
%A A095078 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095079
%S A095079 19,43,53,79,103,107,109,367,379,431,439,443,463,487,491,499,751,
%T A095079 863,887,983,1013,1279,1471,1531,1663,1759,1783,1787,1789,1951,1979,
%U A095079 1999,2011,2027,2029,3067,3581,3823,4027,5119,6079,6911,7039,7103
%N A095079 Primes with two 0-bits in their binary expansion.
%Y A095079 Cf. A095059.
%H A095079 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095079 nonn
%O A095079 1,1
%A A095079 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095060
%S A095060 1,2,2,3,3,9,16,25,50,83,150,286,540,975,1865,3515,6588,12620,23835,
%T A095060 45486,86811,165822,317770,608517,1170182,2254124,4342530,8383468,
%U A095060 16197159,31335332,60680818,117633364,228260489
%N A095060 Number of fibeven primes (A095080) in range ]2^n,2^(n+1)].
%C A095060 As expected, the ratio of a(n)/A036378(n) seems to approach (sqrt(5)-1)/2 (= 0.6180339887...): 1, 1, 1, 0.6, 0.42857, 0.69231, 0.69565, 0.5814, 0.66667, 0.60584, 0.58824, 0.61638, 0.61927, 0.60484, 0.61551, 0.61569, 0.61289, 0.61893, 0.61693, 0.61813, 0.61859, 0.61824, 0.61858, 0.61727, 0.6178, 0.61829, 0.61795, 0.61816, 0.61804, 0.61808, 0.61804, 0.61803, 0.61805
%Y A095060 a(n) = A036378(n)-A095061(n) = A095062(n)+A095067(n).
%H A095060 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095060 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095060 nonn
%O A095060 1,2
%A A095060 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095080
%S A095080 2,3,5,7,11,13,23,29,31,37,41,47,71,73,79,83,89,97,107,109,113,131,
%T A095080 139,149,151,157,167,173,181,191,193,199,223,227,233,241,251,257,
%U A095080 269,277,283,293,311,317,337,353,359,367,379,397,401,409,419,421
%N A095080 Fibeven primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with zero.
%Y A095080 Intersect of A000040 & A022342. Union of A095082 & A095087. Cf. A095060, A095081.
%H A095080 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095080 nonn
%O A095080 1,1
%A A095080 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095061
%S A095061 0,0,0,2,4,4,7,18,25,54,105,178,332,637,1165,2194,4161,7770,14800,
%T A095061 28100,53525,102394,195938,377301,723938,1391620,2684760,5178439,
%U A095061 10010119,19362205,37501838,72702221,141062816
%N A095061 Number of fibodd primes (A095081) in range ]2^n,2^(n+1)].
%C A095061 As expected, the ratio of a(n)/A036378(n) seems to approach 1-((sqrt(5)-1)/2) (= 0.381966011250...): 0, 0, 0, 0.4, 0.57143, 0.30769, 0.30435, 0.4186, 0.33333, 0.39416, 0.41176, 0.38362, 0.38073, 0.39516, 0.38449, 0.38431, 0.38711, 0.38107, 0.38307, 0.38187, 0.38141, 0.38176, 0.38142, 0.38273, 0.3822, 0.38171, 0.38205, 0.38184, 0.38196, 0.38192, 0.38196, 0.38197, 0.38195
%Y A095061 a(n) = A036378(n)-A095060(n) = A095066(n)+A095069(n).
%H A095061 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095061 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095061 nonn
%O A095061 1,4
%A A095061 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095081
%S A095081 17,19,43,53,59,61,67,101,103,127,137,163,179,197,211,229,239,263,
%T A095081 271,281,307,313,331,347,349,373,383,389,433,449,457,467,491,499,
%U A095081 509,569,577,593,601,619,643,653,661,677,739,773,787,797,821,823
%N A095081 Fibodd primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with one.
%Y A095081 Intersect of A000040 & A003622. Union of A095086 & A095089. Cf. A095061, A095080, A095281.
%H A095081 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095081 nonn
%O A095081 1,1
%A A095081 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095062
%S A095062 1,1,2,1,2,7,12,14,27,50,91,178,335,611,1156,2147,4042,7831,14724,
%T A095062 28227,53736,102482,196303,376121,723408,1393572,2683465,5180304,
%U A095062 10009707,19366479,37509260,72706948,141074303
%N A095062 Number of fib00 primes (A095082) in range ]2^n,2^(n+1)].
%Y A095062 a(n) = A095060(n)-A095067(n) = A095065(n)+A095068(n).
%H A095062 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095062 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095062 nonn
%O A095062 1,3
%A A095062 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095082
%S A095082 3,5,11,13,29,37,47,71,73,79,89,97,107,113,131,139,149,157,173,181,
%T A095082 191,199,223,233,241,251,257,283,293,317,359,367,401,409,419,443,
%U A095082 461,479,487,503,521,547,563,571,587,613,631,647,673,683,691,733
%N A095082 Fib00 primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with two zeros.
%Y A095082 Cf. A095062. Intersect of A000040 & A026274. Union of A095085 & A095088.
%H A095082 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095082 nonn
%O A095082 1,1
%A A095082 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095065
%S A095065 0,1,1,1,1,4,9,6,19,28,54,109,210,373,707,1316,2497,4827,9127,17467,
%T A095065 33212,63161,121404,232455,446846,860466,1658020,3200462,6184814,
%U A095065 11971998,23184215,44934259,87179855
%N A095065 Number of fib000 primes (A095085) in range ]2^n,2^(n+1)].
%Y A095065 a(n) = A095062(n)-A095068(n). Cf. A095066-A095067.
%H A095065 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095065 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095065 nonn
%O A095065 1,6
%A A095065 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095085
%S A095085 5,13,29,47,73,89,97,107,131,149,157,173,191,199,233,241,251,293,
%T A095085 317,419,461,479,487,521,547,563,631,673,683,691,733,751,809,827,
%U A095085 877,911,919,937,953,971,1013,1021,1039,1063,1097,1123,1249,1259
%N A095085 Fib000 primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with three zeros.
%Y A095085 Intersect of A000040 & A095097. Cf. A095065.
%H A095085 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095085 nonn
%O A095085 1,1
%A A095085 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095066
%S A095066 0,0,0,1,3,1,6,9,15,34,63,114,206,386,725,1366,2601,4803,9144,17331,
%T A095066 33106,63067,121112,233785,447721,860033,1659656,3200843,6188292,
%U A095066 11966122,23175696,44928209,87187514
%N A095066 Number of fib001 primes (A095086) in range ]2^n,2^(n+1)].
%Y A095066 a(n) = A095061(n)-A095069(n). Cf. A095065 & A095067.
%H A095066 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095066 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095066 nonn
%O A095066 1,5
%A A095066 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095086
%S A095086 19,43,53,61,103,137,163,179,197,229,239,263,281,307,331,349,383,
%T A095086 433,467,509,569,577,619,653,739,773,797,823,839,857,883,907,941,
%U A095086 967,1009,1051,1061,1069,1103,1129,1153,1171,1187,1213,1229,1289
%N A095086 Fib001 primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with two zeros and final 1.
%Y A095086 Intersect of A000040 & A095098. Cf. A095066.
%H A095086 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095086 nonn
%O A095086 1,1
%A A095086 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095067
%S A095067 0,1,0,2,1,2,4,11,23,33,59,108,205,364,709,1368,2546,4789,9111,17259,
%T A095067 33075,63340,121467,232396,446774,860552,1659065,3203164,6187452,
%U A095067 11968853,23171558,44926416,87186186
%N A095067 Number of fib010 primes (A095087) in range ]2^n,2^(n+1)].
%Y A095067 a(n) = A095060(n)-A095062(n).
%H A095067 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095067 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095067 nonn
%O A095067 1,4
%A A095067 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095087
%S A095087 7,23,31,41,83,109,151,167,193,227,269,277,311,337,353,379,397,421,
%T A095087 431,439,463,523,541,557,599,607,617,641,659,701,709,719,727,743,
%U A095087 761,769,811,829,853,863,887,929,947,997,1031,1049,1091,1117,1151
%N A095087 Fib010 primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with zero, one and zero.
%Y A095087 Intersect of A000040 & A035336. Cf. A095067.
%H A095087 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095087 nonn
%O A095087 1,1
%A A095087 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095068
%S A095068 1,0,1,0,1,3,3,8,8,22,37,69,125,238,449,831,1545,3004,5597,10760,
%T A095068 20524,39321,74899,143666,276562,533106,1025445,1979842,3824893,7394481,
%U A095068 14325045,27772689,53894448
%N A095068 Number of fib100 primes (A095088) in range ]2^n,2^(n+1)].
%Y A095068 a(n) = A095062(n)-A095065(n).
%H A095068 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095068 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095068 nonn
%O A095068 1,6
%A A095068 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095088
%S A095088 3,11,37,71,79,113,139,181,223,257,283,359,367,401,409,443,503,571,
%T A095088 587,613,647,757,859,977,1019,1087,1163,1181,1223,1231,1291,1307,
%U A095088 1367,1409,1451,1511,1553,1579,1613,1621,1663,1697,1723,1867,1901
%N A095088 Fib100 primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends with one and two final zeros.
%Y A095088 Intersect of A000040 & A035337. Cf. A095068.
%H A095088 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095088 nonn
%O A095088 1,1
%A A095088 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095069
%S A095069 0,0,0,1,1,3,1,9,10,20,42,64,126,251,440,828,1560,2967,5656,10769,
%T A095069 20419,39327,74826,143516,276217,531587,1025104,1977596,3821827,7396083,
%U A095069 14326142,27774012,53875302
%N A095069 Number of fib101 primes (A095089) in range ]2^n,2^(n+1)].
%Y A095069 a(n) = A095061(n)-A095066(n).
%H A095069 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095069 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095069 nonn
%O A095069 1,6
%A A095069 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095089
%S A095089 17,59,67,101,127,211,271,313,347,373,389,449,457,491,499,593,601,
%T A095089 643,661,677,787,821,881,983,991,1033,1093,1109,1237,1279,1321,1381,
%U A095089 1423,1499,1559,1567,1601,1609,1669,1753,1787,1847,1889,1931,1999
%N A095089 Fib101 primes, i.e. primes p whose Zeckendorf-expansion A014417(p) ends as one, zero, one.
%Y A095089 Intersect of A000040 & A095099. Cf. A095069.
%H A095089 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095089 nonn
%O A095089 1,1
%A A095089 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095063
%S A095063 1,1,1,3,4,7,14,22,41,70,133,261,433,800,1468,2883,5445,10033,19388,
%T A095063 36902,70168,134005,256771,493088,947153,1822376,3514806,6780667,
%U A095063 13103439,25351723,49085715,95166843,184656849
%N A095063 Number of fibodious primes (A095083) in range ]2^n,2^(n+1)].
%Y A095063 a(n) = A036378(n)-A095064(n).
%H A095063 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095063 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095063 nonn
%O A095063 1,4
%A A095063 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095083
%S A095083 2,3,5,13,17,19,31,41,43,59,61,71,73,79,89,103,107,113,131,151,167,
%T A095083 173,179,181,191,197,211,227,229,233,239,251,257,269,293,307,313,
%U A095083 347,349,353,367,383,401,419,431,433,449,457,463,467,479,487,491
%N A095083 Fibodious primes, i.e. primes p whose Zeckendorf-expansion A014417(p) contains an odd number of 1-fibits.
%Y A095083 Intersect of A000040 & A020899. Cf. A095084, A095063.
%H A095083 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095083 nonn
%O A095083 1,1
%A A095083 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095064
%S A095064 0,1,1,2,3,6,9,21,34,67,122,203,439,812,1562,2826,5304,10357,19247,
%T A095064 36684,70168,134211,256937,492730,946967,1823368,3512484,6781240,
%U A095064 13103839,25345814,49096941,95168742,184666456
%N A095064 Number of fibevil primes (A095084) in range ]2^n,2^(n+1)].
%Y A095064 a(n) = A036378(n)-A095063(n).
%H A095064 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095064 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095064 nonn
%O A095064 1,4
%A A095064 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095084
%S A095084 7,11,23,29,37,47,53,67,83,97,101,109,127,137,139,149,157,163,193,
%T A095084 199,223,241,263,271,277,281,283,311,317,331,337,359,373,379,389,
%U A095084 397,409,421,439,443,461,499,503,521,547,557,563,577,593,601,607
%N A095084 Fibevil primes, i.e. primes p whose Zeckendorf-expansion A014417(p) contains an even number of 1-fibits.
%Y A095084 Intersect of A000040 & A095096. Cf. A095083, A095064.
%H A095084 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095084 nonn
%O A095084 1,1
%A A095084 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095092
%S A095092 1,1
%N A095092 Number of 4k+3 primes whose Legendre-vector is a Dyck-path (A095102) in range ]2^n,2^(n+1)].
%Y A095092 a(n) = A095008(n)-A095093(n). Cf. A095090.
%H A095092 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095092 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095092 nonn
%O A095092 1,1
%A A095092 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095102
%S A095102 3,7
%N A095102 Odd primes p for which all sums Sum_{i=1..u} L(i/p) (with u ranging from 1 to (p-1)) are nonnegative, where L(i/p) is Legendre symbol of i and p, defined to be 1 if i is a quadratic residue (mod p) and -1 if i is a quadratic non-residue (mod p).
%C A095102 All 4k+3 primes whose Legendre-vector (cf. A055094) forms a valid Dyck-path (cf. A014486).
%Y A095102 Intersect of A000040 & A095100. Subset of A080114 (see comments there). Complement of A095103 in A002145. a(n) = 4*A095272(n)+3. Cf. A095092.
%H A095102 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095102 nonn
%O A095102 1,1
%A A095102 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095093
%S A095093 0,0
%N A095093 Number of 4k+3 primes whose Legendre-vector is not Dyck-path (A095103) in range ]2^n,2^(n+1)].
%Y A095093 a(n) = A095008(n)-A095092(n).
%H A095093 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095093 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095093 nonn
%O A095093 1,1
%A A095093 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095103
%S A095103 0
%N A095103 4k+3 primes whose Legendre-vector is not valid Dyck-path.
%Y A095103 Intersect of A000040 & A095101. Complement of A095102 in A002145. Diving indices: A095108. a(n) = 4*A095273(n)+3. Cf. also A095093.
%H A095103 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095103 nonn
%O A095103 1,1
%A A095103 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095094
%S A095094 1,2
%N A095094 Number of A080114-primes in range ]2^n,2^(n+1)].
%Y A095094 a(n) = A036378(n)-A095095(n).
%H A095094 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095094 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095094 nonn
%O A095094 1,2
%A A095094 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A080114
%S A080114 3,5,7
%N A080114 Odd primes p for which all sums Sum_{i=1..u} L(i/p) (with u ranging from 1 to (p-1)/2) are nonnegative, where L(i/p) is Legendre symbol of i and p, which is defined to be 1 if i is a quadratic residue (mod p) and -1 if i is a quadratic non-residue (mod p).
%Y A080114 Intersect of A000040 & A0xxxxx. Subset: A095102. Complement of A080115 in A000040. Cf. A095094.
%H A080114 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A080114 nonn
%O A080114 1,1
%A A080114 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Feb 11 2003
%I A095095
%S A095095 0,0
%N A095095 Number of A080115-primes in range ]2^n,2^(n+1)].
%Y A095095 a(n) = A036378(n)-A095094(n).
%H A095095 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095095 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095095 nonn
%O A095095 1,1
%A A095095 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A080115
%S A080115 2
%N A080115 Primes not in A080114.
%Y A080115 Complement of A080114 in A000040. Cf. A095095.
%H A080115 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A080115 nonn
%O A080115 1,1
%A A080115 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Feb 11 2003
%I A095104
%S A095104 0,0
%N A095104 Diving index of the nth 4k+3 prime (A002145(n)).
%C A095104 Diving index of an odd number n is the first integer u > 1 where Sum_{i=1..u} J(i/n) results -1, and zero if never. Here J(i/n) is Jacobi symbol of i and n, which reduces to a Legendre symbol L(i/n) when n is a prime.
%Y A095104 a(n)=A095105(n)+1 modulo A002145(n). Cf. A095106, A095108 (same sequence with zeros removed), A095269.
%H A095104 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095104 nonn
%O A095104 1,1
%A A095104 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095108
%S A095108 0
%N A095108 Diving index of the nth diving 4k+3 prime (A095103(n)).
%Y A095108 Non-zero terms of A095104. Cf. A095271.
%H A095108 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095108 nonn
%O A095108 1,1
%A A095108 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095105
%S A095105 2,6
%N A095105 Length of max. Dyck path prefix in the Legendre-vector of the nth 4k+3 prime (A002145(n)).
%Y A095105 a(n)=A095104(n)-1 modulo A002145(n). Cf. A095107, A095270.
%H A095105 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095105 nonn
%O A095105 1,1
%A A095105 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095106
%S A095106 0,0
%N A095106 Sum of diving indices of all 4k+3 primes in range ]2^n,2^(n+1)].
%Y A095106 Cf. A095104, A095107, A095109.
%H A095106 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095106 nonn
%O A095106 1,1
%A A095106 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095107
%S A095107 2,6
%N A095107 Sum of max Dyck path prefix lengths of all 4k+3 primes in range ]2^n,2^(n+1)].
%Y A095107 Cf. A095105, A095106, A095110.
%H A095107 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095107 nonn
%O A095107 1,1
%A A095107 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095272
%S A095272 0,1
%N A095272 a(n) = (A095102(n)-3)/4.
%Y A095272 Complement of A095273 in A095278, subset of A095274.
%H A095272 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095272 nonn
%O A095272 1,1
%A A095272 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095273
%S A095273 0
%N A095273 a(n) = (A095103(n)-3)/4.
%Y A095273 Complement of A095272 in A095278, subset of A095275.
%H A095273 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095273 nonn
%O A095273 1,1
%A A095273 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095280
%S A095280 3,11,17,19,29,37,43,53,59,61,67,71,79,97,101,103,113,127,131,137,
%T A095280 139,163,173,179,181,197,199,211,223,229,239,241,257,263,271,281,
%U A095280 283,307,313,317,331,347,349,359,367,373,383,389,401,409,419,433
%N A095280 Lower Wythoff Primes, i.e. primes in A000201.
%C A095280 Contains all primes p whose Zeckendorf-expansion A014417(p) ends with an even number of 0's.
%Y A095280 Intersect of A000040 & A000201. Complement of A095281 in A000040. Cf. A095080, A095083, A095084, A095290.
%H A095280 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095280 nonn
%O A095280 1,1
%A A095280 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095290
%S A095290 1,0,1,3,5,8,14,30,40,86,162,289,541,1017,1881,3527,6652,12641,23855,
%T A095290 45455,86753,165844,317363,609942,1171377,2253588,4343268,8381084,
%U A095290 16198859,31329311,60683252,117637523,228259189
%N A095290 Number of Lower Wythoff Primes (A095280) in range ]2^n,2^(n+1)].
%C A095090 As expected, the ratio of a(n)/A036378(n) seems to approach (sqrt(5)-1)/2 (= 0.6180339887...): 1, 0, 0.5, 0.6, 0.714286, 0.615385, 0.608696, 0.697674, 0.533333, 0.627737, 0.635294, 0.622845, 0.620413, 0.630893, 0.620792, 0.617796, 0.618848, 0.619961, 0.617445, 0.617713, 0.618181, 0.618323, 0.617789, 0.618717, 0.618428, 0.618142, 0.618057, 0.617987, 0.618105, 0.617965, 0.618065, 0.618053, 0.618047
%Y A095290 a(n) = A036378(n)-A095291(n). Cf. A095060, A095291.
%H A095290 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095290 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095290 nonn
%O A095290 1,4
%A A095290 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095281
%S A095281 2,5,7,13,23,31,41,47,73,83,89,107,109,149,151,157,167,191,193,227,
%T A095281 233,251,269,277,293,311,337,353,379,397,421,431,439,463,479,523,
%U A095281 541,547,557,599,607,617,641,659,683,691,701,709,719,727,733,743
%N A095281 Upper Wythoff Primes, i.e. primes in A001950.
%C A095281 Contains all primes p whose Zeckendorf-expansion A014417(p) ends with an odd number of 0's.
%Y A095281 Intersect of A000040 & A001950. Complement of A095280 in A000040. Cf. A095081, A095083, A095084, A095290.
%H A095281 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095281 nonn
%O A095281 1,1
%A A095281 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095291
%S A095291 0,2,1,2,2,5,9,13,35,51,93,175,331,595,1149,2182,4097,7749,14780,
%T A095291 28131,53583,102372,196345,375876,722743,1392156,2684022,5180823,
%U A095291 10008419,19368226,37499404,72698062,141064116
%N A095291 Number of Upper Wythoff Primes (A095281) in range ]2^n,2^(n+1)].
%C A095291 As expected, the ratio of a(n)/A036378(n) seems to approach 1-((sqrt(5)-1)/2) (= 0.381966011250...): 0, 1, 0.5, 0.4, 0.285714, 0.384615, 0.391304, 0.302326, 0.466667, 0.372263, 0.364706, 0.377155, 0.379587, 0.369107, 0.379208, 0.382204, 0.381152, 0.380039, 0.382555, 0.382287, 0.381819, 0.381677, 0.382211, 0.381283, 0.381572, 0.381858, 0.381943, 0.382013, 0.381895, 0.382035, 0.381935, 0.381947, 0.381953
%C A095291 Also expected, the ratio a(n)/A095061(n) seems to approach 1: 1, 0, 0, 1, 0.5, 1.25, 1.28571, 0.72222, 1.4, 0.94444, 0.88571, 0.98315, 0.99699, 0.93407, 0.98627, 0.99453, 0.98462, 0.9973, 0.99865, 1.0011, 1.00108, 0.99979, 1.00208, 0.99622, 0.99835, 1.00039, 0.99973, 1.00046, 0.99983, 1.00031, 0.99994, 0.99994, 1.00001
%Y A095291 a(n) = A036378(n)-A095290(n). Cf. A095061, A095290.
%H A095291 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095291 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095291 nonn
%O A095291 1,2
%A A095291 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095282
%S A095282 2,3,11,19,43,47,59,67,79,83,107,131,139,163,179,191,211,227,239,
%T A095282 251,271,283,307,331,347,367,379,419,431,443,463,467,491,499,523,
%U A095282 547,563,571,587,619,643,659,683,691,719,739,751,787,811,827,859
%N A095282 Primes whose binary-expansion ends with an even number of 1's.
%Y A095282 Intersect of A000040 & (complement of A079523). Complement of A095283 in A000040. Cf. A027699, A095292.
%H A095282 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095282 nonn
%O A095282 1,1
%A A095282 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095292
%S A095292 1,0,1,1,3,4,9,14,23,47,88,152,295,540,1004,1933,3572,6805,12909,
%T A095292 24461,46767,89481,171327,328638,631302,1215243,2342291,4520976,8736608,
%U A095292 16899331,32727125,63446234,123106396
%N A095292 Number of A095282-primes in range ]2^n,2^(n+1)].
%Y A095292 a(n) = A036378(n)-A095293(n). Cf. A095006.
%H A095292 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095292 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095292 nonn
%O A095292 1,5
%A A095292 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095283
%S A095283 5,7,13,17,23,29,31,37,41,53,61,71,73,89,97,101,103,109,113,127,137,
%T A095283 149,151,157,167,173,181,193,197,199,223,229,233,241,257,263,269,
%U A095283 277,281,293,311,313,317,337,349,353,359,373,383,389,397,401,409
%N A095283 Primes whose binary-expansion ends with an odd number of 1's.
%Y A095283 Intersect of A000040 & A079523. Complement of A095282 in A000040. Cf. A027697, A095293.
%H A095283 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095283 nonn
%O A095283 1,1
%A A095283 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095293
%S A095293 0,2,1,4,4,9,14,29,52,90,167,312,577,1072,2026,3776,7177,13585,25726,
%T A095293 49125,93569,178735,342381,657180,1262818,2430501,4684999,9040931,
%U A095293 17470670,33798206,65455531,126889351,246216909
%N A095293 Number of A095283-primes in range ]2^n,2^(n+1)].
%C A095293 As expected, the ratio a(n)/A095292(n) seems to approach 2: 0, 0, 1, 4, 1.33333, 2.25, 1.55556, 2.07143, 2.26087, 1.91489, 1.89773, 2.05263, 1.95593, 1.98519, 2.01793, 1.95344, 2.00924, 1.99633, 1.99287, 2.0083, 2.00075, 1.99746, 1.99841, 1.99971, 2.00034, 2.00001, 2.00018, 1.99977, 1.99971, 1.99997, 2.00004, 1.99995, 2.00003
%Y A095293 a(n) = A036378(n)-A095292(n). Cf. A095005.
%H A095293 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095293 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095293 nonn
%O A095293 1,2
%A A095293 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095320
%S A095320 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095320 89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,
%U A095320 179,181,191,193,197,199,211,223,227,229,233,239,241,251,263,269
%N A095320 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 3.
%C A095320 Differs from primes (A000040) first time at n=55, where a(55)=263, while A000040(55)=257, as 257 whose binary expansion is 100000001, with 2 1-bits and 7 0-bits is the first prime excluded from this sequence. Note that 129 (10000001 in binary, 2 1-bits and 6 0-bits) is not prime.
%Y A095320 Complement of A095321 in A000040. Subset: A095316.A095330.
%H A095320 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095320 nonn
%O A095320 1,1
%A A095320 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095330
%S A095330 1,2,2,5,7,13,23,42,71,122,241,412,789,1413,2770,4859,9545,16955,
%T A095330 34039,60484,121241,216830,441223,785885,1597803,2867949,5874665,
%U A095330 10544609,21636090,39034399,80414166,145210901,299284792
%N A095330 Number of A095320-primes in range ]2^n,2^(n+1)].
%C A095330 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 1, 1, 0.976744, 0.946667, 0.890511, 0.945098, 0.887931, 0.904817, 0.876551, 0.914191, 0.851112, 0.88799, 0.831535, 0.881041, 0.82195, 0.863934, 0.808416, 0.858898, 0.797191, 0.84356, 0.786657, 0.835979, 0.777517, 0.825576, 0.769947, 0.819026, 0.76292, 0.81036
%Y A095330 a(n) = A036378(n)-A095331(n).
%H A095330 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095330 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095330 nonn
%O A095330 1,2
%A A095330 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095321
%S A095321 257,521,577,641,769,1031,1033,1049,1061,1091,1093,1097,1153,1217,
%T A095321 1283,1289,1297,1409,1553,1601,2053,2069,2081,2083,2089,2113,2129,
%U A095321 2179,2309,2593,2689,3089,3137,3329,4099,4111,4129,4133,4139,4153
%N A095321 Primes in whose binary expansion the number of 1-bits is <= number of 0-bits minus 3.
%Y A095321 Complement of A095320 in A000040. Subset of A095317. Cf. also A095331.
%H A095321 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095321 nonn
%O A095321 1,1
%A A095321 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095331
%S A095331 0,0,0,0,0,0,0,1,4,15,14,52,83,199,260,850,1204,3435,4596,13102,19095,
%T A095331 51386,72485,199933,296317,777795,1152625,3017298,4571188,11663138,
%U A095331 17768490,45124684,70038513
%N A095331 Number of A095321-primes in range ]2^n,2^(n+1)].
%C A095331 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0, 0, 0.023256, 0.053333, 0.109489, 0.054902, 0.112069, 0.095183, 0.123449, 0.085809, 0.148888, 0.11201, 0.168465, 0.118959, 0.17805, 0.136066, 0.191584, 0.141102, 0.202809, 0.15644, 0.213343, 0.164021, 0.222483, 0.174424, 0.230053, 0.180974, 0.23708, 0.18964
%Y A095331 a(n) = A036378(n)-A095330(n).
%H A095331 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095331 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095331 nonn
%O A095331 1,9
%A A095331 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095316
%S A095316 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095316 89,97,101,103,107,109,113,127,139,149,151,157,163,167,173,179,181,
%U A095316 191,197,199,211,223,227,229,233,239,241,251,263,269,271,277,281
%N A095316 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 2.
%C A095316 Differs from primes (A000040) first time at n=32, where a(32)=139, while A000040(32)=131, as 131 whose binary expansion is 10000011, with 3 1-bits and 5 0-bits is the first prime excluded from this sequence.
%Y A095316 Complement of A095317 in A000040. Subset of A095320. Subset: A095074. Cf. also A095326.
%H A095316 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095316 nonn
%O A095316 1,1
%A A095316 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095326
%S A095326 1,2,2,5,7,13,20,42,65,122,203,412,718,1413,2381,4859,8266,16955,
%T A095326 28995,60484,105524,216830,376969,785885,1383287,2867949,5044969,
%U A095326 10544609,18699214,39034399,69349061,145210901,259051224
%N A095326 Number of A095316-primes in range ]2^n,2^(n+1)].
%C A095326 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 1, 0.869565, 0.976744, 0.866667, 0.890511, 0.796078, 0.887931, 0.823394, 0.876551, 0.785809, 0.851112, 0.769002, 0.831535, 0.750485, 0.82195, 0.751938, 0.808416, 0.73382, 0.797191, 0.730306, 0.786657, 0.717911, 0.777517, 0.713512, 0.769947, 0.706327, 0.76292, 0.701421
%Y A095326 a(n) = A036378(n)-A095327(n).
%H A095326 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095326 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095326 nonn
%O A095326 1,2
%A A095326 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095317
%S A095317 131,137,193,257,521,523,547,577,593,641,643,673,769,773,1031,1033,
%T A095317 1049,1061,1091,1093,1097,1153,1217,1283,1289,1297,1409,1553,1601,
%U A095317 2053,2063,2069,2081,2083,2087,2089,2099,2113,2129,2131,2137,2153
%N A095317 Primes in whose binary expansion the number of 1-bits is <= number of 0-bits minus 2.
%Y A095317 Complement of A095316 in A000040. Subset: A095321. Subset of A095071. Cf. also A095327.
%H A095317 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095317 nonn
%O A095317 1,1
%A A095317 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095327
%S A095327 0,0,0,0,0,0,3,1,10,15,52,52,154,199,649,850,2483,3435,9640,13102,
%T A095327 34812,51386,136739,199933,510833,777795,1982321,3017298,7508064,
%U A095327 11663138,28833595,45124684,110272081
%N A095327 Number of A095317-primes in range ]2^n,2^(n+1)].
%Y A095327 a(n) = A036378(n)-A095326(n).
%H A095327 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095327 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095327 nonn
%O A095327 1,7
%A A095327 Antti Karttunen (his-firstname.his-surname(AT)iki.fi)
%C A095327 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0, 0.130435, 0.023256, 0.133333, 0.109489, 0.203922, 0.112069, 0.176606, 0.123449, 0.214191, 0.148888, 0.230998, 0.168465, 0.249515, 0.17805, 0.248062, 0.191584, 0.26618, 0.202809, 0.269694, 0.213343, 0.282089, 0.222483, 0.286488, 0.230053, 0.293673, 0.23708, 0.298579, Jun 03 2004
%I A095074
%S A095074 2,3,5,7,11,13,19,23,29,31,37,41,43,47,53,59,61,71,79,83,89,101,103,
%T A095074 107,109,113,127,139,149,151,157,163,167,173,179,181,191,197,199,
%U A095074 211,223,227,229,233,239,241,251,271,283,307,311,313,317,331,347
%N A095074 Primes in whose binary expansion the number of 0-bits is less than or equal to number of 1-bits.
%C A095074 Differs from primes (A000040) first time at n=7, where a(7)=19, while A000040(7)=17, as 17 whose binary expansion is 10001, with 2 1-bits and 3 0-bits is the first prime excluded from this sequence.
%Y A095074 Complement of A095071 in A000040. Subset of A095316. Subset: A095070. Differs from A057447 first time at n=18, where a(n)=71, while A057447(18)=67. Cf. A095054.
%H A095074 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095074 nonn
%O A095074 1,1
%A A095074 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095054
%S A095054 1,2,2,4,7,10,20,32,65,97,203,334,718,1130,2381,3953,8266,13911,28995,
%T A095054 49564,105524,178910,376969,650703,1383287,2380394,5044969,8780393,
%U A095054 18699214,32618497,69349061,121625616,259051224
%N A095054 Number of primes with #0-bits <= #1-bits (A095074) in range ]2^n,2^(n+1)].
%Y A095054 a(n) = A095020(n) + (if n is odd) A095018((n+1)/2).
%C A095054 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 1, 0.769231, 0.869565, 0.744186, 0.866667, 0.708029, 0.796078, 0.719828, 0.823394, 0.700993, 0.785809, 0.692415, 0.769002, 0.682246, 0.750485, 0.673552, 0.751938, 0.667037, 0.73382, 0.660064, 0.730306, 0.652924, 0.717911, 0.647431, 0.713512, 0.643394, 0.706327, 0.639006, 0.701421
%H A095054 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095054 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095054 nonn
%O A095054 1,2
%A A095054 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095071
%S A095071 17,67,73,97,131,137,193,257,263,269,277,281,293,337,353,389,401,
%T A095071 449,521,523,547,577,593,641,643,673,769,773,1031,1033,1039,1049,
%U A095071 1051,1061,1063,1069,1091,1093,1097,1109,1123,1129,1153,1163,1171
%N A095071 Zero-bit dominant primes, i.e. primes whose binary expansion contains more 0's than 1's.
%Y A095071 Complement of A095074 in A000040. Subsets: A095317, A095072. Subset of A095075. Cf. also A095019.
%H A095071 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095071 nonn
%O A095071 1,1
%A A095071 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095019
%S A095019 0,0,0,1,0,3,3,11,10,40,52,130,154,482,649,1756,2483,6479,9640,24022,
%T A095019 34812,89306,136739,335115,510833,1265350,1982321,4781514,7508064,
%U A095019 18079040,28833595,68709969,110272081
%N A095019 Number of zero-bit dominant primes (A095071) in range ]2^n,2^(n+1)].
%Y A095019 Cf. A095018.
%C A095019 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0, 0.230769, 0.130435, 0.255814, 0.133333, 0.291971, 0.203922, 0.280172, 0.176606, 0.299007, 0.214191, 0.307585, 0.230998, 0.317754, 0.249515, 0.326448, 0.248062, 0.332963, 0.26618, 0.339936, 0.269694, 0.347076, 0.282089, 0.352569, 0.286488, 0.356606, 0.293673, 0.360994, 0.298579
%H A095019 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095019 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095019 nonn
%O A095019 1,6
%A A095019 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095070
%S A095070 3,5,7,11,13,19,23,29,31,43,47,53,59,61,71,79,83,89,101,103,107,109,
%T A095070 113,127,151,157,167,173,179,181,191,199,211,223,227,229,233,239,
%U A095070 241,251,271,283,307,311,313,317,331,347,349,359,367,373,379,383
%N A095070 One-bit dominant primes, i.e. primes whose binary expansion contains more 1's than 0's.
%Y A095070 Intersect of A000040 & A072600. Complement of A095075 in A000040. Subset of A095074. Subsets: A095286, A095073. Cf. A095020.
%H A095070 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095070 nonn
%O A095070 1,1
%A A095070 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095020
%S A095020 1,2,2,4,5,10,16,32,48,97,175,334,529,1130,1850,3953,6276,13911,23248,
%T A095020 49564,81622,178910,300311,650703,1091809,2380394,4062176,8780393,
%U A095020 15021634,32618497,56134342,121625616,209889612
%N A095020 Number of one-bit dominant primes (A095070) in range ]2^n,2^(n+1)].
%C A095020 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 0.714286, 0.769231, 0.695652, 0.744186, 0.64, 0.708029, 0.686275, 0.719828, 0.606651, 0.700993, 0.610561, 0.692415, 0.583868, 0.682246, 0.601734, 0.673552, 0.581618, 0.667037, 0.584595, 0.660064, 0.57642, 0.652924, 0.578057, 0.647431, 0.573186, 0.643394, 0.571734, 0.639006, 0.568309
%Y A095020 Cf. A095018.
%H A095020 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095020 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095020 nonn
%O A095020 1,2
%A A095020 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095075
%S A095075 2,17,37,41,67,73,97,131,137,139,149,163,193,197,257,263,269,277,
%T A095075 281,293,337,353,389,401,449,521,523,541,547,557,563,569,577,587,
%U A095075 593,601,613,617,641,643,647,653,659,661,673,677,709,769,773,787
%N A095075 Primes in whose binary expansion the number of 1-bits is less than or equal to number of 0-bits.
%Y A095075 Complement of A095070 in A000040. Subset: A095071. Subset of A095287. Cf. A095055.
%H A095075 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095075 nonn
%O A095075 1,1
%A A095075 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095055
%S A095055 0,0,0,1,2,3,7,11,27,40,80,130,343,482,1180,1756,4473,6479,15387,
%T A095055 24022,58714,89306,213397,335115,802311,1265350,2965114,4781514,11185644,
%U A095055 18079040,42048314,68709969,159433693
%N A095055 Number of primes with #1-bits <= #0-bits (A095075) in range ]2^n,2^(n+1)].
%C A095055 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0.285714, 0.230769, 0.304348, 0.255814, 0.36, 0.291971, 0.313725, 0.280172, 0.393349, 0.299007, 0.389439, 0.307585, 0.416132, 0.317754, 0.398266, 0.326448, 0.418382, 0.332963, 0.415405, 0.339936, 0.42358, 0.347076, 0.421943, 0.352569, 0.426814, 0.356606, 0.428266, 0.360994, 0.431691
%Y A095055 a(n) = A095019(n) + (if n is odd) A095018((n+1)/2).
%H A095055 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095055 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095055 nonn
%O A095055 1,5
%A A095055 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004
%I A095286
%S A095286 3,7,11,13,23,29,31,43,47,53,59,61,79,103,107,109,127,151,157,167,
%T A095286 173,179,181,191,199,211,223,227,229,233,239,241,251,311,317,347,
%U A095286 349,359,367,373,379,383,431,439,443,461,463,467,479,487,491,499
%N A095286 Primes in whose binary expansion the number of 1-bits is > 1 + number of 0-bits.
%Y A095286 Complement of A095287 in A000040. Subset of A095070. Subset: A095314. Cf. also A095296.
%H A095286 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095286 nonn
%O A095286 1,1
%A A095286 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095296
%S A095296 1,1,2,3,5,5,16,21,48,69,175,229,529,768,1850,2860,6276,10252,23248,
%T A095296 36563,81622,133739,300311,491193,1091809,1816561,4062176,6772098,
%U A095296 15021634,25284670,56134342,94895078,209889612
%N A095296 Number of A095286-primes in range ]2^n,2^(n+1)].
%C A095296 Ratios a(n)/A036378(n) converge as: 1, 0.5, 1, 0.6, 0.714286, 0.384615, 0.695652, 0.488372, 0.64, 0.50365, 0.686275, 0.493534, 0.606651, 0.476427, 0.610561, 0.500963, 0.583868, 0.502795, 0.601734, 0.496874, 0.581618, 0.498624, 0.584595, 0.498259, 0.57642, 0.498269, 0.578057, 0.499347, 0.573186, 0.498736, 0.571734, 0.498567, 0.568309
%C A095296 Ratios a(n)/A095335(n) converge as: 1, 1, 1, 1.5, 1.25, 0.625, 0.842105, 0.954545, 1.116279, 1.014706, 1.100629, 0.974468, 0.985102, 0.909953, 0.966562, 1.003861, 0.984008, 1.011245, 1.00445, 0.987575, 0.991822, 0.994512, 0.988408, 0.993061, 0.99389, 0.9931, 0.99673, 0.997392, 0.997286, 0.994955, 0.995265, 0.994285, 0.996248
%Y A095296 a(n) = A036378(n)-A095297(n). Cf. A095298.
%H A095296 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095296 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095296 nonn
%O A095296 1,3
%A A095296 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095287
%S A095287 2,5,17,19,37,41,67,71,73,83,89,97,101,113,131,137,139,149,163,193,
%T A095287 197,257,263,269,271,277,281,283,293,307,313,331,337,353,389,397,
%U A095287 401,409,419,421,433,449,457,521,523,541,547,557,563,569,577,587
%N A095287 Primes in whose binary expansion the number of 1-bits is <= 1 + number of 0-bits.
%Y A095287 Complement of A095286 in A000040. Subset: A095075. Subset of A095315. Cf. also A095297.
%H A095287 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095287 nonn
%O A095287 1,1
%A A095287 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095297
%S A095297 0,1,0,2,2,8,7,22,27,68,80,235,343,844,1180,2849,4473,10138,15387,
%T A095297 37023,58714,134477,213397,494625,802311,1829183,2965114,6789809,
%U A095297 11185644,25412867,42048314,95440507,159433693
%N A095297 Number of A095287-primes in range ]2^n,2^(n+1)].
%C A095297 Ratios a(n)/A036378(n) converge as: 0, 0.5, 0, 0.4, 0.285714, 0.615385, 0.304348, 0.511628, 0.36, 0.49635, 0.313725, 0.506466, 0.393349, 0.523573, 0.389439, 0.499037, 0.416132, 0.497205, 0.398266, 0.503126, 0.418382, 0.501376, 0.415405, 0.501741, 0.42358, 0.501731, 0.421943, 0.500653, 0.426814, 0.501264, 0.428266, 0.501433, 0.431691
%C A095297 Ratios a(n)/A095334(n) converge as: 1, 1, 1, 0.666667, 0.666667, 1.6, 1.75, 1.047619, 0.84375, 0.985507, 0.833333, 1.026201,1.023881, 1.098958, 1.057348, 0.996154, 1.023336, 0.98888, 0.993351,1.012581, 1.011595, 1.005518, 1.016781, 1.006987, 1.008436, 1.006948,1.004514, 1.002615, 1.003668, 1.00507, 1.006392, 1.005748, 1.004982
%Y A095297 a(n) = A036378(n)-A095296(n). Cf. A095298.
%H A095297 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095297 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095297 nonn
%O A095297 1,4
%A A095297 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095314
%S A095314 7,23,29,31,47,59,61,79,103,107,109,127,191,223,239,251,311,317,347,
%T A095314 349,359,367,373,379,383,431,439,443,461,463,467,479,487,491,499,
%U A095314 503,509,607,631,701,719,727,733,743,751,757,761,823,827,829,859
%N A095314 Primes in whose binary expansion the number of 1-bits is > 2 + number of 0-bits.
%Y A095314 Complement of A095315 in A000040. Subset of A095286. Subset: A095318. Cf. also A095334.
%H A095314 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095314 nonn
%O A095314 1,1
%A A095314 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095334
%S A095334 0,1,0,3,3,5,4,21,32,69,96,229,335,768,1116,2860,4371,10252,15490,
%T A095334 36563,58041,133739,209875,491193,795599,1816561,2951789,6772098,
%U A095334 11144763,25284670,41781268,94895078,158643268
%N A095334 Number of A095314-primes in range ]2^n,2^(n+1)].
%C A095334 Ratios a(n)/A036378(n) converge as: 0, 0.5, 0, 0.6, 0.428571, 0.384615, 0.173913, 0.488372, 0.426667, 0.50365, 0.376471, 0.493534, 0.384174, 0.476427, 0.368317, 0.500963, 0.406642, 0.502795, 0.400932, 0.496874, 0.413586, 0.498624, 0.408549, 0.498259, 0.420036, 0.498269, 0.420047, 0.499347, 0.425255, 0.498736, 0.425546, 0.498567, 0.429551
%C A095334 Ratios a(n)/A095297(n) converge as: 1, 1, 1, 1.5, 1.5, 0.625, 0.571429, 0.954545, 1.185185, 1.014706, 1.2, 0.974468, 0.976676, 0.909953, 0.945763, 1.003861, 0.977197, 1.011245, 1.006694, 0.987575, 0.988538, 0.994512, 0.983496, 0.993061, 0.991634, 0.9931, 0.995506, 0.997392, 0.996345, 0.994955, 0.993649, 0.994285, 0.995042
%Y A095334 a(n) = A036378(n)-A095335(n). Cf. A095298.
%H A095334 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095334 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095334 nonn
%O A095334 1,4
%A A095334 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095315
%S A095315 2,3,5,11,13,17,19,37,41,43,53,67,71,73,83,89,97,101,113,131,137,
%T A095315 139,149,151,157,163,167,173,179,181,193,197,199,211,227,229,233,
%U A095315 241,257,263,269,271,277,281,283,293,307,313,331,337,353,389,397
%N A095315 Primes in whose binary expansion the number of 1-bits is <= 2 + number of 0-bits.
%Y A095315 Complement of A095314 in A000040. Subset: A095287. Subset of A095319. Cf. also A095335.
%H A095315 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095315 nonn
%O A095315 1,1
%A A095315 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095335
%S A095335 1,1,2,2,4,8,19,22,43,68,159,235,537,844,1914,2849,6378,10138,23145,
%T A095335 37023,82295,134477,303833,494625,1098521,1829183,4075501,6789809,
%U A095335 15062515,25412867,56401388,95440507,210680037
%N A095335 Number of A09515-primes in range ]2^n,2^(n+1)].
%C A095335 Ratios a(n)/A036378(n) converge as: 1, 0.5, 1, 0.4, 0.571429, 0.615385, 0.826087, 0.511628, 0.573333, 0.49635, 0.623529, 0.506466, 0.615826, 0.523573, 0.631683, 0.499037, 0.593358, 0.497205, 0.599068, 0.503126, 0.586414, 0.501376, 0.591451, 0.501741, 0.579964, 0.501731, 0.579953, 0.500653, 0.574745, 0.501264, 0.574454, 0.501433, 0.570449
%C A095335 Ratios a(n)/A095296(n) converge as: 1, 1, 1, 0.666667, 0.8,1.6, 1.1875, 1.047619, 0.895833, 0.985507, 0.908571, 1.026201,1.015123, 1.098958, 1.034595, 0.996154, 1.016252, 0.98888, 0.99557,1.012581, 1.008245, 1.005518, 1.011728, 1.006987, 1.006148, 1.006948,1.00328, 1.002615, 1.002721, 1.00507, 1.004757, 1.005748, 1.003766
%Y A095335 a(n) = A036378(n)-A095334(n).
%H A095335 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095335 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095335 nonn
%O A095335 1,3
%A A095335 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095318
%S A095318 31,47,59,61,127,191,223,239,251,367,379,383,431,439,443,463,479,
%T A095318 487,491,499,503,509,607,631,701,719,727,733,743,751,757,761,823,
%U A095318 827,829,859,863,877,883,887,911,919,941,947,953,967,971,983,991
%N A095318 Primes in whose binary expansion the number of 1-bits is > 3 + number of 0-bits.
%Y A095318 Complement of A095319 in A000040. Subset of A095314. Subset: A095322. Cf. also A095328.
%H A095318 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095318 nonn
%O A095318 1,1
%A A095318 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095328
%S A095328 0,0,0,1,3,1,4,13,32,35,96,124,335,466,1116,1717,4371,6380,15490,
%T A095328 23904,58041,88200,209875,331769,795599,1258386,2951789,4741344,11144763,
%U A095328 17964801,41781268,68371012,158643268
%N A095328 Number of A095318-primes in range ]2^n,2^(n+1)].
%C A095328 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0.428571, 0.076923, 0.173913, 0.302326, 0.426667, 0.255474, 0.376471, 0.267241, 0.384174, 0.289082, 0.368317, 0.300753, 0.406642, 0.312898, 0.400932, 0.324844, 0.413586, 0.328839, 0.408549, 0.336542, 0.420036, 0.345166, 0.420047, 0.349607, 0.425255, 0.354353, 0.425546, 0.359213, 0.429551
%C A095328 Ratios a(n)/A095055(n) converge as: 1, 1, 1, 1, 1.5, 0.333333, 0.571429, 1.181818, 1.185185, 0.875, 1.2, 0.953846, 0.976676, 0.966805, 0.945763, 0.97779, 0.977197, 0.98472, 1.006694, 0.995088, 0.988538, 0.987616, 0.983496, 0.990015, 0.991634, 0.994496, 0.995506, 0.991599, 0.996345, 0.993681, 0.993649, 0.995067, 0.995042
%Y A095328 a(n) = A036378(n)-A095329(n).
%H A095328 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095328 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095328 nonn
%O A095328 1,5
%A A095328 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095319
%S A095319 2,3,5,7,11,13,17,19,23,29,37,41,43,53,67,71,73,79,83,89,97,101,103,
%T A095319 107,109,113,131,137,139,149,151,157,163,167,173,179,181,193,197,
%U A095319 199,211,227,229,233,241,257,263,269,271,277,281,283,293,307,311
%N A095319 Primes in whose binary expansion the number of 1-bits is <= 3 + number of 0-bits.
%Y A095319 Complement of A095318 in A000040. Subset of A095323, subset: A095315. A095329.
%H A095319 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095319 nonn
%O A095319 1,1
%A A095319 Antti Karttunen (his-firstname.his-surname(AT)iki.fi)
%C A095319 Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with 5 1-bits and no 0-bits is the first prime excluded from this sequence., Jun 03 2004
%I A095329
%S A095329 1,2,2,4,4,12,19,30,43,102,159,340,537,1146,1914,3992,6378,14010,
%T A095329 23145,49682,82295,180016,303833,654049,1098521,2387358,4075501,8820563,
%U A095329 15062515,32732736,56401388,121964573,210680037
%N A095329 Number of A095319-primes in range ]2^n,2^(n+1)].
%C A095329 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 0.571429, 0.923077, 0.826087, 0.697674, 0.573333, 0.744526, 0.623529, 0.732759, 0.615826, 0.710918, 0.631683, 0.699247, 0.593358, 0.687102, 0.599068, 0.675156, 0.586414, 0.671161, 0.591451, 0.663458, 0.579964, 0.654834, 0.579953, 0.650393, 0.574745, 0.645647, 0.574454, 0.640787, 0.570449
%C A095329 Ratios a(n)/A095020(n) converge as: 1, 1, 1, 1, 0.8, 1.2,1.1875, 0.9375, 0.895833, 1.051546, 0.908571, 1.017964, 1.015123,1.014159, 1.034595, 1.009866, 1.016252, 1.007117, 0.99557, 1.002381,1.008245, 1.006182, 1.011728, 1.005142, 1.006148, 1.002926, 1.00328,1.004575, 1.002721, 1.003502, 1.004757, 1.002787, 1.003766
%Y A095329 a(n) = A036378(n)-A095328(n).
%H A095329 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095329 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095329 nonn
%O A095329 1,2
%A A095329 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095322
%S A095322 31,127,191,223,239,251,367,379,383,431,439,443,463,479,487,491,499,
%T A095322 503,509,751,863,887,983,991,1013,1019,1021,1151,1277,1279,1399,1439,
%U A095322 1471,1487,1499,1511,1523,1531,1663,1723,1759,1783,1787,1789,1823
%N A095322 Primes in whose binary expansion the number of 1-bits is > 4 + number of 0-bits.
%Y A095322 Complement of A095323 in A000040. Subset of A095318. Subset: A095284. Cf. also A095324.
%H A095322 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095322 nonn
%O A095322 1,1
%A A095322 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095324
%S A095324 0,0,0,1,0,1,4,13,8,35,44,124,150,466,701,1717,2326,6380,9354,23904,
%T A095324 34443,88200,134780,331769,508200,1258386,1957824,4741344,7424464,
%U A095324 17964801,28737086,68371012,109643089
%N A095324 Number of A095322-primes in range ]2^n,2^(n+1)].
%C A095324 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0, 0.076923, 0.173913, 0.302326, 0.106667, 0.255474, 0.172549, 0.267241, 0.172018, 0.289082, 0.231353, 0.300753, 0.216392, 0.312898, 0.242112, 0.324844, 0.245432, 0.328839, 0.262367, 0.336542, 0.268304, 0.345166, 0.278603, 0.349607, 0.283298, 0.354353, 0.29269, 0.359213, 0.296876
%C A095324 Ratios a(n)/A095019(n) converge as: 1, 1, 1, 1, 1, 0.333333, 1.333333, 1.181818, 0.8, 0.875, 0.846154, 0.953846, 0.974026, 0.966805, 1.080123, 0.97779, 0.93677, 0.98472, 0.970332, 0.995088, 0.9894, 0.987616, 0.985673, 0.990015, 0.994846, 0.994496, 0.987642, 0.991599, 0.988865, 0.993681, 0.996653, 0.995067, 0.994296
%Y A095324 a(n) = A036378(n)-A095325(n).
%H A095324 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095324 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095324 nonn
%O A095324 1,7
%A A095324 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095323
%S A095323 2,3,5,7,11,13,17,19,23,29,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T A095323 97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,181,
%U A095323 193,197,199,211,227,229,233,241,257,263,269,271,277,281,283,293
%N A095323 Primes in whose binary expansion the number of 1-bits is <= 4 + number of 0-bits.
%C A095323 Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with 5 1-bits and no 0-bits is the first prime excluded from this sequence. Note that 15 (1111 in binary) is not prime.
%Y A095323 Complement of A095322 in A000040. Subset of A095285. subset: A095319. A095325.
%H A095323 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095323 nonn
%O A095323 1,1
%A A095323 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095325
%S A095325 1,2,2,4,7,12,19,30,67,102,211,340,722,1146,2329,3992,8423,14010,
%T A095325 29281,49682,105893,180016,378928,654049,1385920,2387358,5069466,
%U A095325 8820563,18782814,32732736,69445570,121964573,259680216
%N A095325 Number of A095323-primes in range ]2^n,2^(n+1)].
%C A095325 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 1, 0.923077, 0.826087, 0.697674, 0.893333, 0.744526, 0.827451, 0.732759, 0.827982, 0.710918, 0.768647, 0.699247, 0.783608, 0.687102, 0.757888, 0.675156, 0.754568, 0.671161, 0.737633, 0.663458, 0.731696, 0.654834, 0.721397, 0.650393, 0.716702, 0.645647, 0.70731, 0.640787, 0.703124
%C A095325 Ratios a(n)/A095054(n) converge as: 1, 1, 1, 1, 1, 1.2, 0.95, 0.9375, 1.030769, 1.051546, 1.039409, 1.017964, 1.005571,1.014159, 0.97816, 1.009866, 1.018993, 1.007117, 1.009864, 1.002381,1.003497, 1.006182, 1.005197, 1.005142, 1.001903, 1.002926, 1.004856,1.004575, 1.004471, 1.003502, 1.001392, 1.002787, 1.002428
%Y A095325 a(n) = A036378(n)-A095324(n).
%H A095325 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095325 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095325 nonn
%O A095325 1,2
%A A095325 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095284
%S A095284 127,191,223,239,251,383,479,503,509,751,863,887,983,991,1013,1019,
%T A095284 1021,1279,1471,1531,1663,1759,1783,1787,1789,1951,1979,1999,2011,
%U A095284 2027,2029,2039,2543,2551,2557,2687,2879,2927,2939,2999,3023,3037
%N A095284 Primes in whose binary expansion the number of 1-bits is > 5 + number of 0-bits.
%Y A095284 Complement of A095285 in A000040. Subset of A095322. Subset: A095312.Cf. also A095286, A095294.
%H A095284 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095284 nonn
%O A095284 1,1
%A A095284 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095294
%S A095294 0,0,0,0,0,1,4,4,8,15,44,47,150,236,701,863,2326,3298,9354,12933,
%T A095294 34443,51300,134780,199410,508200,769127,1957824,2978179,7424464,
%U A095294 11590386,28737086,44867556,109643089
%N A095294 Number of A095284-primes in range ]2^n,2^(n+1)].
%C A095294 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0.076923, 0.173913, 0.093023, 0.106667, 0.109489, 0.172549, 0.101293, 0.172018, 0.146402, 0.231353, 0.151165, 0.216392, 0.161746, 0.242112, 0.175754, 0.245432, 0.191264, 0.262367, 0.202279, 0.268304, 0.210966, 0.278603, 0.219599, 0.283298, 0.228618, 0.29269, 0.235729, 0.296876
%C A095294 Ratios a(n)/A095327(n) converge as: 1, 1, 1, 1, 1, 0,1.333333, 4., 0.8, 1, 0.846154, 0.903846, 0.974026, 1.18593, 1.080123,1.015294, 0.93677, 0.960116, 0.970332, 0.987101, 0.9894, 0.998326, 0.985673, 0.997384, 0.994846, 0.988856, 0.987642, 0.987035, 0.988865, 0.993762, 0.996653, 0.994302, 0.994296
%Y A095294 a(n) = A036378(n)-A095295(n). Cf. also A095329, A095052, A095053
%H A095294 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095294 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095294 nonn
%O A095294 1,7
%A A095294 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095285
%S A095285 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095285 89,97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,
%U A095285 181,193,197,199,211,227,229,233,241,257,263,269,271,277,281,283
%N A095285 Primes in whose binary expansion the number of 1-bits is <= 5 + number of 0-bits.
%C A095285 Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence. Note that 63 (111111 in binary) is not prime.
%Y A095285 Complement of A095284 in A000040. Subset: A095323. Subset of A095313, from which it differs first time at n=42, where a(42)=193 (11000001 in binary) while A095313(42)=191 (10111111 in binary). Cf. also A095286, A095295.
%H A095285 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095285 nonn
%O A095285 1,1
%A A095285 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095295
%S A095295 1,2,2,5,7,12,19,39,67,122,211,417,722,1376,2329,4846,8423,17092,
%T A095295 29281,60653,105893,216916,378928,786408,1385920,2876617,5069466,
%U A095295 10583728,18782814,39107151,69445570,145468029,259680216
%N A095295 Number of A095285-primes in range ]2^n,2^(n+1)].
%C A095295 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 0.923077, 0.826087, 0.906977, 0.893333, 0.890511, 0.827451, 0.898707, 0.827982, 0.853598, 0.768647, 0.848835, 0.783608, 0.838254, 0.757888, 0.824246, 0.754568, 0.808736, 0.737633, 0.797721, 0.731696, 0.789034, 0.721397, 0.780401, 0.716702, 0.771382, 0.70731, 0.764271, 0.703124
%C A095295 Ratios a(n)/A095326(n) converge as: 1, 1, 1, 1, 1, 0.923077, 0.95, 0.928571, 1.030769, 1, 1.039409, 1.012136, 1.005571, 0.973815, 0.97816, 0.997325, 1.018993, 1.00808, 1.009864, 1.002794,1.003497, 1.000397, 1.005197, 1.000665, 1.001903, 1.003022, 1.004856,1.00371, 1.004471, 1.001864, 1.001392, 1.001771, 1.002428
%Y A095295 a(n) = A036378(n)-A095294(n). A095052, A095053
%H A095295 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095295 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095295 nonn
%O A095295 1,2
%A A095295 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095312
%S A095312 127,383,479,503,509,991,1019,1021,1279,1471,1531,1663,1759,1783,
%T A095312 1787,1789,1951,1979,1999,2011,2027,2029,2039,3067,3581,3583,3823,
%U A095312 3967,4027,4079,4091,4093,5087,5119,5503,5623,5879,6007,6011,6047
%N A095312 Primes in whose binary expansion the number of 1-bits is > 6 + number of 0-bits.
%Y A095312 Complement of A095313 in A000040. Subset of A095284. Cf. also A095332.
%H A095312 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095312 nonn
%O A095312 1,1
%A A095312 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095332
%S A095332 0,0,0,0,0,1,0,4,3,15,9,47,73,236,251,863,1180,3298,4284,12933,18598,
%T A095332 51300,73371,199410,292156,769127,1131645,2978179,4533090,11590386,
%U A095332 17623347,44867556,69537472
%N A095332 Number of A095312-primes in range ]2^n,2^(n+1)].
%C A095332 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0.076923, 0, 0.093023, 0.04, 0.109489, 0.035294, 0.101293, 0.083716, 0.146402, 0.082838, 0.151165, 0.109778, 0.161746, 0.110884, 0.175754, 0.132525, 0.191264, 0.142826, 0.202279, 0.154244, 0.210966, 0.161036, 0.219599, 0.172971, 0.228618, 0.179496, 0.235729, 0.188283
%C A095332 Ratios a(n)/A095331(n) converge as: 1, 1, 1, 1, 1, 0, 1,4, 0.75, 1, 0.642857, 0.903846, 0.879518, 1.18593, 0.965385,1.015294, 0.980066, 0.960116, 0.932115, 0.987101, 0.973972, 0.998326,1.012223, 0.997384, 0.985958, 0.988856, 0.981798, 0.987035, 0.991666, 0.993762, 0.991831, 0.994302, 0.992846
%Y A095332 a(n) = A036378(n)-A095333(n).
%H A095332 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095332 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095332 nonn
%O A095332 1,8
%A A095332 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095313
%S A095313 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095313 89,97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,
%U A095313 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N A095313 Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.
%C A095313 Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence.
%Y A095313 Complement of A095312 in A000040. Subset: A095285, from which it differs first time at n=42, where a(42)=191 (10111111 in binary), while A095285(42)=193 (11000001 in binary).Cf. also A095333.
%H A095313 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095313 nonn
%O A095313 1,1
%A A095313 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095333
%S A095333 1,2,2,5,7,12,23,39,72,122,246,417,799,1376,2779,4846,9569,17092,
%T A095333 34351,60653,121738,216916,440337,786408,1601964,2876617,5895645,
%U A095333 10583728,21674188,39107151,80559309,145468029,299785833
%N A095333 Number of A095313-primes in range ]2^n,2^(n+1)].
%C A095333 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 0.923077, 1, 0.906977, 0.96, 0.890511, 0.964706, 0.898707, 0.916284, 0.853598, 0.917162, 0.848835, 0.890222, 0.838254, 0.889116, 0.824246, 0.867475, 0.808736, 0.857174, 0.797721, 0.845756, 0.789034, 0.838964, 0.780401, 0.827029, 0.771382, 0.820504, 0.764271, 0.811717
%C A095333 Ratios a(n)/A095330(n) converge as: 1, 1, 1, 1, 1, 0.923077, 1, 0.928571, 1.014085, 1, 1.020747, 1.012136, 1.012674, 0.973815, 1.003249, 0.997325, 1.002514, 1.00808, 1.009166, 1.002794,1.004099, 1.000397, 0.997992, 1.000665, 1.002604, 1.003022, 1.003571,1.00371, 1.001761, 1.001864, 1.001805, 1.001771, 1.001674
%Y A095333 a(n) = A036378(n)-A095332(n).
%H A095333 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095333 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095333 nonn
%O A095333 1,2
%A A095333 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095298
%S A095298 0,1,2,8,15,30,67,154,302,611,1280,2546,5207,10447,21123,42783,85726,
%T A095298 173102,347243,698544,1401784,2813930,5644165,11328192,22712057,45538473,
%U A095298 91288241,182965151,366691833,734702678,1471976078,2948741819,5906481468
%N A095298 Sum of 1-bits between the most and least significant bits summed for all primes in range ]2^n,2^(n+1)].
%e A095298 a(1)=0, as only prime in range ]2,4] is 3, which has no space between its most and least significant digits. a(2)=1, as in that range there are two primes 5 (101 in binary) and 7 (111 in binary) and summing their middle bits we get 1. a(3)=2, as there are again two primes, 11 (1011 in binary), and 13 (1101 in binary), and summing the bits in the middle we get total 2.
%Y A095298 Cf. A095297, A095334, A095353.
%H A095298 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095298 nonn
%O A095298 1,3
%A A095298 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095336
%S A095336 1,3,3,13,20,41,76,176,325,638,1353,2533,5223,10186,20504,40775,80661,
%T A095336 163765,318602,649948,1268922,2571531,5082895,10217300,20327307,40399966,
%U A095336 82164918,160343669,324931245,640501167,1290990369,2567150515,5145601743
%N A095336 Sum of 1-fibits in Zeckendorf-expansion A014417(p) summed for all primes p in range ]2^n,2^(n+1)].
%e A095336 a(1)=1, as only prime in range ]2,4] is 3, whose Fibonacci-representation is 100. In the next range we have primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively, thus a(2)=3.
%Y A095336 Cf. A095298, A095353.
%H A095336 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095336 nonn
%O A095336 1,2
%A A095336 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095353
%S A095353 0,0,1,3,2,7,7,14,23,35,56,94,155,243,402,614,1061,1656,2689,4295,
%T A095353 6938,11176,18095,29102,46907,75703,122174,197494,317987,514611,829595,
%U A095353 1340861,2166008,3497040,5645418,9120129,14733126,23803219,38460014
%N A095353 Sum of 1-fibits in Zeckendorf-expansion A014417(p) summed for all primes p in range [Fib(n+1),Fib(n+2)[ (where Fib = A000045).
%e A095353 a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100. a(4)=3, as in [5,8[ there are primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively, and we have three 1-fibits in total. a(5)=2, as in [8,13[ there is only one prime 11, with Zeckendorf-representation 10100.
** DISCARD THE LAST NON-ZERO ENTRY BEFORE SUBMITTING, IT'S INCORRECT **
%Y A095353 Cf. A095336.
%H A095353 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095353 nonn
%O A095353 1,4
%A A095353 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A095354
%S A095354 0,0,1,2,1,3,3,5,7,11,16,24,37,55,84,126,198,297,458,704,1087,1674,
%T A095354 2602,4029,6263,9738,15186,23705,36981,57909,90550,142033,222855,
%U A095354 349862,549903,865019,1361581,2145191,3381318,5334509,8419527,13298631
%N A095354 Number of primes p such that Fib(n+1) <= p < Fib(n+2), (where Fib = A000045).
%e A095354 I.e. gives the number of primes whose Zeckendorf-expansion is n fibits long. a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100. a(4)=2, as in [5,8[ there are primes 5 and 7. a(5)=1, as in [8,13[ there is only one prime 11, and a(6)=3 as in [13,21[ there are primes 13,17,19.
** DISCARD THE LAST NON-ZERO ENTRY BEFORE SUBMITTING, IT'S INCORRECT **
%Y A095354 Cf. A095353, A036378.
%H A095354 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095354 nonn
%O A095354 1,4
%A A095354 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 03 2004
%I A080165
%S A080165 2,5,11,17,19,23,37,41,43,47,67,71,73,79,83,89,131,137,139,149,151,
%T A080165 157,163,167,173,179,181,191,257,263,269,271,277,281,283,293,307,
%U A080165 311,313,317,331,337,347,349,353,359,367,373,379,383,521,523,541
%N A080165 Primes in whose binary expansion the most significant bits begin as 10...
%Y A080165 Complement of A080166 in A000040. Cf. A095765.
%H A080165 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A080165 nonn
%O A080165 1,1
%A A080165 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 03 2003
%I A080166
%S A080166 3,7,13,29,31,53,59,61,97,101,103,107,109,113,127,193,197,199,211,
%T A080166 223,227,229,233,239,241,251,389,397,401,409,419,421,431,433,439,
%U A080166 443,449,457,461,463,467,479,487,491,499,503,509,769,773,787,797
%N A080166 Primes in whose binary expansion the most significant bits begin as 11...
%Y A080166 Complement of A080165 in A000040. Cf. A095766.
%H A080166 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A080166 nonn
%O A080166 1,1
%A A080166 Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 03 2003
%I A095765
%S A095765 0,1,1,3,4,6,12,22,38,70,130,237,441,825,1539,2897,5453,10335,19556,
%T A095765 37243,70938,135555,259586,497790,956126,1839597,3544827,6839282,
%U A095765 13212389,25552386,49472951,95883938,186011076
%N A095765 Number of primes whose binary expansion begins as '10' (A080165) in range ]2^n,2^(n+1)].
%C A095765 I.e. number of primes p such that 2^n < p < (2^n + 2^(n-1)).
%C A095765 Ratio a(n)/A036378(n) converges as: 0, 0.5, 0.5, 0.6, 0.571429, 0.461538, 0.521739, 0.511628, 0.506667, 0.510949, 0.509804, 0.510776, 0.505734, 0.511787, 0.507921, 0.507444, 0.507303, 0.506866, 0.506173, 0.506115, 0.505487, 0.505395, 0.505318, 0.504951, 0.504786, 0.504588, 0.504437, 0.504301, 0.50415, 0.504016, 0.503887, 0.503763, 0.503654
%C A095765 Ratio a(n)/A095766(n) converges as: 0, 1, 1, 1.5, 1.333333, 0.857143, 1.090909, 1.047619, 1.027027, 1.044776, 1.04, 1.044053, 1.023202, 1.048285, 1.032193, 1.030228, 1.029645, 1.027847, 1.025001, 1.024764, 1.022191, 1.021815, 1.021501, 1.020003, 1.019331, 1.01852, 1.017908, 1.017353, 1.016737, 1.016195, 1.015669, 1.015164, 1.014723
%C A095765 I think this explains also the bias present in ratios shown at A095297, A095298, etc.
%Y A095765 a(n) = A036378(n)-A095766(n).
%H A095765 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095765 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095765 nonn
%O A095765 1,4
%A A095765 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095766
%S A095766 1,1,1,2,3,7,11,21,37,67,125,227,431,787,1491,2812,5296,10055,19079,
%T A095766 36343,69398,132661,254122,488028,937994,1806147,3482463,6722625,
%U A095766 12994889,25145151,48709705,94451647,183312229
%N A095766 Number of primes whose binary expansion begins as '11' (A080166) in range ]2^n,2^(n+1)].
%C A095766 I.e. number of primes p such that (2^n + 2^(n-1)) < p < 2^(n+1).
%C A095766 Ratio a(n)/A036378(n) converges as: 1, 0.5, 0.5, 0.4, 0.428571, 0.538462, 0.478261, 0.488372, 0.493333, 0.489051, 0.490196, 0.489224, 0.494266, 0.488213, 0.492079, 0.492556, 0.492697, 0.493134, 0.493827, 0.493885, 0.494513, 0.494605, 0.494682, 0.495049, 0.495214, 0.495412, 0.495563, 0.495699, 0.49585, 0.495984, 0.496113, 0.496237, 0.496346
%Y A095766 a(n) = A036378(n)-A095765(n).
%H A095766 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095766 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095766 nonn
%O A095766 1,4
%A A095766 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A016041
%S A016041 3,5,7,17,31,73,107,127,257,313,443,1193,1453,1571,1619,1787,1831,
%T A016041 1879,4889,5113,5189,5557,5869,5981,6211,6827,7607,7759,7919,8191,
%U A016041 17377,18097,18289,19433,19609,19801,21157,22541,22669,22861,23581
%N A016041 Primes whose binary expansion is palindromic.
%Y A016041 Intersection of A000040 & A048701. The first row of array A095749. Cf. A095741.
%H A016041 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A016041 nonn
%O A016041 1,1
%A A016041 Robert G. Wilson v (rgwv(AT)rgwv.com),
%I A095741
%S A095741 2,2,3,3,7,12,23,40,94,142,271,480,856,1721,3099,5572
%N A095741 Number of base-2 palindromic primes (A016041) in range ]2^2n,2^(2n+1)].
%C A095741 Note that there are no such primes in any range ]2^(2n-1),2^2n], as all even-length binary palindromes are divisible by three (cf. A048702).
%C A095741 Ratio a(n)/A036378(2n) converges as: 1, 0.4, 0.230769, 0.069767, 0.051095, 0.025862, 0.014268, 0.007006, 0.00461, 0.00193, 0.00101, 0.000487, 0.000235, 0.000127, 0.000061, 0.000029
%Y A095741 Bisection of the first diagonal of triangle A095759. Cf. also A095731.
%H A095741 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095741 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095741 nonn
%O A095741 1,1
%A A095741 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095743
%S A095743 2,11,13,19,23,29,37,41,47,59,61,67,89,97,103,131,137,157,167,173,
%T A095743 181,191,193,199,211,223,227,229,239,251,277,281,317,337,349,367,
%U A095743 373,383,401,419,431,463,467,479,487,491,503,509,521,563,569,577
%N A095743 Primes p for which A037888(p)=1, i.e. primes whose binary expansion is almost symmetric, needing just a one-bit flip to become palindrome.
%Y A095743 The second row of array A095749. Cf. A095753, A095748.
%H A095743 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095743 nonn
%O A095743 1,1
%A A095743 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095753
%S A095753 0,0,2,3,5,4,15,18,32,33,63,81,119,144,256,318,527,640,1029,1281,
%T A095753 2236,2566,4273,5410,8261,10610,16868,21084,33943,43104,68218,88493,
%U A095753 136343
%N A095753 Number of almost base-2 palindromic primes (A095743) in range ]2^n,2^(n+1)].
%C A095753 Ratio a(n)/A036378(n) converges as: 0, 0, 1, 0.6, 0.714286, 0.307692, 0.652174, 0.418605, 0.426667, 0.240876, 0.247059, 0.174569, 0.136468, 0.08933, 0.084488, 0.055702, 0.049028, 0.031388, 0.026634, 0.017408, 0.015933, 0.009567, 0.008318, 0.005488, 0.004361, 0.00291, 0.0024, 0.001555, 0.001295, 0.00085, 0.000695, 0.000465, 0.000369
%C A095753 Ratio a(n)/A095758(n) converges as: 1, 1, 0, 1.5, 1, 1, 3.75, 1.2, 2, 1.375, 1.909091, 1.446429, 1.652778, 1.515789, 1.718121, 1.452055, 1.636646, 1.191806, 1.570992, 1.283567, 1.708174, 1.380312, 1.534842, 1.392177, 1.547004, 1.311334, 1.573801, 1.302205, 1.521016, 1.419202, 1.570938, 1.389237, 1.546084
%Y A095753 The second diagonal of triangle A095759. Cf. A095742.
%H A095753 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095753 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095753 nonn
%O A095753 1,3
%A A095753 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095744
%S A095744 43,53,71,79,83,101,109,113,139,149,163,197,263,269,283,293,307,353,
%T A095744 359,379,389,409,433,439,449,461,499,523,547,571,593,619,643,673,
%U A095744 691,751,773,811,821,839,857,863,881,887,907,983,1013,1031,1049,1063
%N A095744 Primes p for which A037888(p)=2, i.e. primes whose binary expansion needs flips of just two bits to become palindrome.
%Y A095744 The third row of array A095749. Cf. A095754.
%H A095744 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095744 nonn
%O A095744 1,1
%A A095744 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095754
%S A095754 0,0,0,0,2,6,4,15,20,63,62,135,150,398,347,913,895,2196,1907,5151,
%T A095754 4483,11932,10033,26498,22645,59155,49968,130032,108271,283447,233865,
%U A095754 606296,503884
%N A095754 Number of A095744-primes in range ]2^n,2^(n+1)].
%C A095754 Ratio a(n)/A036378(n) converges as: 0, 0, 0, 0, 0.285714, 0.461538, 0.173913, 0.348837, 0.266667, 0.459854, 0.243137, 0.290948, 0.172018, 0.246898, 0.114521, 0.159923, 0.083264, 0.1077, 0.049359, 0.07, 0.031945, 0.044487, 0.019531, 0.026879, 0.011955, 0.016226, 0.007111, 0.009588, 0.004131, 0.005591, 0.002382, 0.003185, 0.001364
%Y A095754 The third diagonal of triangle A095759.
%H A095754 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095754 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095754 nonn
%O A095754 1,5
%A A095754 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095745
%S A095745 151,179,233,241,271,311,331,347,397,421,457,541,557,607,613,631,
%T A095745 659,727,743,809,829,877,929,941,953,997,1009,1039,1051,1151,1171,
%U A095745 1231,1291,1483,1511,1523,1549,1567,1609,1637,1669,1693,1741,1801
%N A095745 Primes p for which A037888(p)=3, i.e. primes whose binary expansion needs flips of just three bits to become palindrome.
%Y A095745 The fourth row of array A095749. Cf. A095755.
%H A095745 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095745 nonn
%O A095745 1,1
%A A095745 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095755
%S A095755 0,0,0,0,0,0,4,7,16,24,88,154,314,479,959,1568,2620,4394,7110,11987,
%T A095755 18434,31444,46474,78790,114464,194921,276169,471971,656213,1123888,
%U A095755 1535212,2648075,3543260
%N A095755 Number of A095745-primes in range ]2^n,2^(n+1)].
%C A095755 Ratio a(n)/A036378(n) converges as: 0, 0, 0, 0, 0, 0, 0.173913, 0.162791, 0.213333, 0.175182, 0.345098, 0.331897, 0.360092, 0.297146, 0.316502, 0.274654, 0.243744, 0.215498, 0.18403, 0.162898, 0.131356, 0.117234, 0.090468, 0.079923, 0.060431, 0.053465, 0.0393, 0.034801, 0.025039, 0.022168, 0.015636, 0.013913, 0.009594
%Y A095755 The fourth diagonal of triangle A095759.
%H A095755 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095755 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095755 nonn
%O A095755 1,7
%A A095755 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095746
%S A095746 599,683,739,797,853,937,977,1087,1103,1223,1307,1427,1459,1597,1613,
%T A095746 1733,2017,2141,2221,2239,2251,2287,2357,2389,2399,2423,2467,2617,
%U A095746 2683,2699,2729,2767,2851,2897,2903,3019,3167,3389,3461,3527,3533
%N A095746 Primes p for which A037888(p)=4, i.e. primes whose binary expansion needs flips of just four bits to become palindrome.
%Y A095746 The fifth row of array A095749. Cf. A095756.
%H A095746 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095746 nonn
%O A095746 1,1
%A A095746 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095756
%S A095756 0,0,0,0,0,0,0,0,7,10,33,56,197,430,773,1482,2737,5769,8912,17912,
%T A095756 26885,55407,77839,158860,214829,441818,575634,1178349,1499574,3096644,
%U A095756 3836084,7918328,9615133
%N A095756 Number of A095746-primes in range ]2^n,2^(n+1)].
%C A095756 Ratio a(n)/A036378(n) converges as: 0, 0, 0, 0, 0, 0, 0, 0, 0.093333, 0.072993, 0.129412, 0.12069, 0.225917, 0.266749, 0.255116, 0.25959, 0.254628, 0.282933, 0.230672, 0.243416, 0.191576, 0.206576, 0.151524, 0.161145, 0.113419, 0.121187, 0.081914, 0.086887, 0.05722, 0.061081, 0.039071, 0.041602, 0.026034
%Y A095756 The fifth diagonal of triangle A095759.
%H A095756 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095756 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095756 nonn
%O A095756 1,9
%A A095756 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095747
%S A095747 3,5,7,11,13,19,23,29,43,53,71,79,83,101,109,113,151,179,233,241,
%T A095747 271,311,331,347,397,421,457,599,683,739,797,853,937,977,1087,1103,
%U A095747 1223,1307,1427,1459,1597,1613,1733,2017,2111,2143,2503,2731,3011
%N A095747 Maximally base-2 asymmetric primes.
%C A095747 Primes p for which A037888(p)=(A070939(p)-2)/2 (here /2 first subtracts 1 if the dividend is odd), i.e. odd primes whose binary expansion is as asymmetric as possible.
%Y A095747 A095757, A095749.
%H A095747 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095747 nonn
%O A095747 1,1
%A A095747 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095757
%S A095757 1,2,2,3,2,6,4,7,7,10,9,26,20,43,27,74,41,112,93,181,167,495,274,
%T A095757 796,558,1232,935,2602,1512,5164,3275,8689,6309
%N A095757 Number of A095747-primes in range ]2^n,2^(n+1)].
%C A095757 Ratio a(n)/A036378(n) converges as: 1, 1, 1, 0.6, 0.285714, 0.461538, 0.173913, 0.162791, 0.093333, 0.072993, 0.035294, 0.056034, 0.022936, 0.026675, 0.008911, 0.012962, 0.003814, 0.005493, 0.002407, 0.00246, 0.00119, 0.001846, 0.000533, 0.000807, 0.000295, 0.000338, 0.000133, 0.000192, 0.000058, 0.000102, 0.000033, 0.000046, 0.000017
%Y A095757 The last non-zero terms from each row of triangle A095759. Bisection: A095760.
%H A095757 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095757 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095757 nonn
%O A095757 1,2
%A A095757 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095760
%S A095760 1,2,2,4,7,9,20,27,41,93,167,274,558,935,1512,3275,6309
%N A095760 Number of A095747-primes in range ]2^(2n-1),2^2n].
%Y A095760 Bisection of A095757, the central diagonal of triangle A095759.
%H A095760 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095760 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095760 nonn
%O A095760 1,2
%A A095760 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095748
%S A095748 17,31,37,41,47,59,61,67,89,97,103,139,149,163,197,263,269,283,293,
%T A095748 307,353,359,379,389,409,433,439,449,461,499,541,557,607,613,631,
%U A095748 659,727,743,809,829,877,929,941,953,997,1009,1039,1051,1151,1171
%N A095748 Almost maximally base-2 asymmetric primes.
%C A095748 Primes p for which A037888(p)=(A070939(p)-4)/2 (here /2 first subtracts 1 if the dividend is odd), i.e. odd primes whose binary expansion contains just two bits mirroring each other (in addition to the most and the least significant bits, which are always 1).
%Y A095748 A095758, A095749, A095743
%H A095748 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095748 nonn
%O A095748 1,1
%A A095748 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095758
%S A095758 0,0,0,2,5,4,4,15,16,24,33,56,72,95,149,219,322,537,655,998,1309,
%T A095758 1859,2784,3886,5340,8091,10718,16191,22316,30372,43425,63699,88186
%N A095758 Number of A095748-primes in range ]2^n,2^(n+1)].
%C A095758 Ratio a(n)/A036378(n) converges as: 0, 0, 0, 0.4, 0.714286, 0.307692, 0.173913, 0.348837, 0.213333, 0.175182, 0.129412, 0.12069, 0.082569, 0.058933, 0.049175, 0.03836, 0.029956, 0.026336, 0.016954, 0.013562, 0.009328, 0.006931, 0.005419, 0.003942, 0.002819, 0.002219, 0.001525, 0.001194, 0.000852, 0.000599, 0.000442, 0.000335, 0.000239
%C A095758 Ratio a(n)/A095753(n) converges as: 1, 1, 0, 0.666667, 1, 1, 0.266667, 0.833333, 0.5, 0.727273, 0.52381, 0.691358, 0.605042, 0.659722, 0.582031, 0.688679, 0.611006, 0.839063, 0.63654, 0.779079, 0.58542, 0.724474, 0.651533, 0.718299, 0.646411, 0.762582, 0.635404, 0.767928, 0.657455, 0.704621, 0.636562, 0.71982, 0.646795
%Y A095758 The penultimate non-zero terms from each row of triangle A095759. Cf. A095757, A095742.
%H A095758 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%H A095758 Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
%K A095758 nonn
%O A095758 1,4
%A A095758 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095742
%S A095742 0,0,2,3,9,16,35,69,148,271,628,1167,2629,4830,10597,20083,42928,
%T A095742 81579,174223,331314,701382,1340756,2825575,5422454,11361615,21873923,
%U A095742 45673361,88161666,183458213,354899159,736343490,1427495050,2954560104
%N A095742 Sum of A037888(p) for all primes p such that 2^n < p < 2^(n+1).
%e A095742 a(1)=0, as only prime in range ]2,4] is 3, which has palindromic binary expansion 11, i.e. A037888(3)=0. a(2)=0, as in range ]4,8] there are two primes 5 (101 in binary) and 7 (111 in binary) so A037888(5) + A037888(7) = 0. a(3)=2, as in range ]8,16] there are two primes, 11 (1011 in binary), and 13 (1101 in binary), thus A037888(11) + A037888(13) = 1+1 = 2.
%C A095742 Ratio a(n)/A036378(n) gives the average asymmetricity ratio for n-bit primes: 0, 0, 1, 0.6, 1.285714, 1.230769, 1.521739, 1.604651, 1.973333, 1.978102, 2.462745, 2.515086, 3.014908, 2.996278, 3.49736, 3.517779, 3.993674, 4.000932, 4.50946, 4.502405, 4.997877, 4.998792, 5.500352, 5.500462, 5.998361, 5.999852, 6.499427, 6.500684, 7.000277, 7.000323, 7.499731, 7.499885, 7.999929, etc. I.e. 2- and 3-bit primes are all palindromes, 4-bit primes need on average just a one-bit flip to become palindromes, etc.
%Y A095742 Cf. A095298, A095732 (sums of similar assymetricity measures for Zeckendorf-expansion), A095753.
%H A095742 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095742 nonn
%O A095742 1,3
%A A095742 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095730
%S A095730 127,197,1949,2137,3323,3821,7253,8117,10243,13183,14947,15131,30941,
%T A095730 31721,39607,43691,49207,54773,62213,66413,70141,70429,70607,71089,
%U A095730 123457,123923,129023,134039,137699,145391,149381,157219,162523,167759
%N A095730 Primes p whose Zeckendorf-expansion A014417(p) is palindromic.
%Y A095730 Intersection of A000040 & A094202. Cf. A095731 for number of occurrences. A095733 shows the corresponding Fibonacci-representations.
%H A095730 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095730 nonn
%O A095730 1,1
%A A095730 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095731
%S A095731 0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,2,2,0,3,3,0,4,8,0,15,4,0,20,42,0,44,
%T A095731 35,0,67,147,0,231,147,0,209,538,0,833,450,0,819,2064,0,1701
%N A095731 Number of such primes p (A095730) such that Fib(n+1) <= p < Fib(n+2) (where Fib = A000045) and p's Zeckendorf-expansion A014417(p) is palindromic.
** DISCARD THE LAST NON-ZERO ENTRY BEFORE SUBMITTING IF IT'S INCORRECT **
%Y A095731 A095732, A095741.
%H A095731 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095731 nonn
%O A095731 1,16
%A A095731 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004
%I A095732
%S A095732 0,0,1,3,1,3,7,10,12,23,31,58,93,171,243,422,634,1142,1684,2971,4406,
%T A095732 7768,11502,20502,30242,53039,79161,138410,207536,362391,544895,947189,
%U A095732 1431794,2473232,3749944,6459373,9823917,16879245,25745781,44112347
%N A095732 Sum of A095734(p) for all primes p such that Fib(n+1) <= p < Fib(n+2) (where Fib = A000045).
%e A095732 a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100, which is just a one fibit-flip away from being a palindrome (i.e. A095734(3)=1). a(4)=3, as in [5,8[ there are primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively, and the other needs one bit-flip and the other two to become palindromes, and 1 + 2 = 3. a(5)=1, as in [8,13[ there is only one prime 11, with Zeckendorf-representation 10100, which needs to have just its least significant fibit flipped from 0 to 1 to become palindrome.
%C A095732 Ratio a(n)/A095354(n) converges as: 1, 1, 1, 1.5, 1, 1, 2.333333, 2, 1.714286, 2.090909, 1.9375, 2.416667, 2.513514, 3.109091, 2.892857, 3.349206, 3.20202, 3.845118, 3.676856, 4.22017, 4.053358, 4.640382, 4.420446, 5.088608, 4.828676, 5.446601, 5.212762, 5.838853, 5.611963, 6.257939, 6.017615, 6.668795, 6.424778, 7.069164, 6.819283, 7.467319, 7.215081, 7.868411, 7.614126, 8.269242
** DISCARD THE LAST NON-ZERO ENTRY BEFORE SUBMITTING IF IT'S INCORRECT **
%Y A095732 Cf. A095730, A095731, A095742 (sums of similar assymetricity measures for binary-expansion).
%H A095732 A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
%K A095732 nonn
%O A095732 1,4
%A A095732 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 06 2004