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[2] != (A095092[2]+A095093[2]), i.e. 1 != (0+0) 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 1 positions. A036378[2] != (A095094[2]+A095095[2]), i.e. 2 != (0+0) 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 1 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. %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 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). %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^n]. %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)]. %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)]. %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. %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 %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 %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 %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 %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 1,1 %A A095094 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 01 2004 %I A080114 %S A080114 3 %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 %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 %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 %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 %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 %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 %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)]. %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)]. %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)]. %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. %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)]. %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.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)]. %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. %Y A095316 Complement of A095317 in A000040. Subset of A095320.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)]. %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.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), 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. %Y A095074 Complement of A095071 in A000040. 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). %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. Subset: A095072. Cf. 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. %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: 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)]. %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. 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)]. %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.A095284. %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)]. %Y A095296 a(n) = A036378(n)-A095297(n). %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.A095285. %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)]. %Y A095297 a(n) = A036378(n)-A095296(n). %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.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)]. %Y A095334 a(n) = A036378(n)-A095335(n). %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.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)]. %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.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)]. %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.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), 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)]. %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.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)]. %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. %Y A095323 Complement of A095322 in A000040.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)]. %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.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)]. %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. %Y A095285 Complement of A095284 in A000040.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)]. %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.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)]. %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. %Y A095313 Complement of A095312 in A000040.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)]. %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