%I A036378
%S A036378 1,2,2,5,7,13,23,43,75,137,255,464,872,1612,3030,5709,10749,20390,38635,73586,140336,268216,513708,985818,1894120,3645744,7027290,13561907,26207278,50697537,98182656
%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) =  A095021(n)+A095022(n)+A095023(n)+A095024(n).
%K A036378 nonn
%O A036378 1,2
%A A036378 Labos E. (labos(AT)ana1.sote.hu), May 13 2004

%I A095005
%S A095005 0,1,2,2,5,8,19,20,48,75,160,242,505,835,1761,2799,5890,10250,20921,36872,74316,134816,267749,492286,977207,1823657,3598657,6779899,13336543,25358424,49763462
%N A095005 Number of odious primes (A027697) in range ]2^n,2^(n+1)].
%Y A095005 a(n) = A036378(n)-A095006(n).
%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), May 28 2004

%I A095006
%S A095006 1,1,0,3,2,5,4,23,27,62,95,222,367,777,1269,2910,4859,10140,17714,36714,66020,133400,245959,493532,916913,1822087,3428633,6782008,12870735,25339113,48419194
%N A095006 Number of evil primes (A027699) in range ]2^n,2^(n+1)].
%Y A095006 a(n) = A036378(n)-A095005(n).
%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), May 28 2004

%I A095007
%S A095007 0,1,1,2,4,6,10,21,38,66,127,233,432,805,1511,2837,5378,10186,19294,36827,70157,133975,256852,492882,946848,1823129,3513599,6780412,13103462,25348870,49090415
%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).
%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), May 28 2004

%I A095008
%S A095008 1,1,1,3,3,7,13,22,37,71,128,231,440,807,1519,2872,5371,10204,19341,36759,70179,134241,256856,492936,947272,1822615,3513691,6781495,13103816,25348667,49092241
%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).
%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), May 28 2004

%I A095009
%S A095009 0,0,0,1,1,4,4,10,18,31,64,115,216,398,752,1413,2692,5092,9642,18355,35089,66907,128431,246479,473201,911650,1756523,3390156,6551387,12673576,24545135
%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.
%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), May 28 2004

%I A095010
%S A095010 1,0,1,1,2,3,7,10,20,35,66,113,218,412,746,1460,2672,5104,9651,18375,35105,67165,128410,246453,473535,911489,1756670,3390856,6552449,12673142,24546849
%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.
%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), May 28 2004

%I A095011
%S A095011 0,1,1,1,3,2,6,11,20,35,63,118,216,407,759,1424,2686,5094,9652,18472,35068,67068,128421,246403,473647,911479,1757076,3390256,6552075,12675294,24545280
%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.
%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), May 28 2004

%I A095012
%S A095012 0,1,0,2,1,4,6,12,17,36,62,118,222,395,773,1412,2699,5100,9690,18384,35074,67076,128446,246483,473737,911126,1757021,3390639,6551367,12675525,24545392
%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.
%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), May 28 2004

%I A095013
%S A095013 0,1,0,3,2,8,10,22,35,67,126,233,438,793,1525,2825,5391,10192,19332,36739,70163,133983,256877,492962,946938,1822776,3513544,6780795,13102754,25349101,49090527
%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).
%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), May 28 2004

%I A095014
%S A095014 1,1,2,2,5,5,13,21,40,70,129,231,434,819,1505,2884,5358,10198,19303,36847,70173,134233,256831,492856,947182,1822968,3513746,6781112,13104524,25348436,49092129
%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).
%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), May 28 2004

%I A095015
%S A095015 0,1,1,2,3,7,11,20,37,69,126,228,434,806,1514,2845,5361,10212,19308,36747,70135,134065,256824,492871,946880,1822913,3513737,6780428,13103565,25348226,49090715
%N A095015 Number of 6k+1 primes (A002476) in range ]2^n,2^(n+1)].
%Y A095015 a(n) = A036378(n)-A095016(n).
%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), May 28 2004

%I A095016
%S A095016 0,1,1,3,4,6,12,23,38,68,129,236,438,806,1516,2864,5388,10178,19327,36839,70201,134151,256884,492947,947240,1822831,3513553,6781479,13103713,25349311,49091941
%N A095016 Number of 6k+5 primes (A007528) in range ]2^n,2^(n+1)].
%Y A095016 a(n) = A036378(n)-A095015(n).
%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), May 28 2004

%I A095017
%S A095017 1,1,1,2,2,3,7,7,12,26,45,70,113,215,355,666,1153,2071,3785,6965,12495,22643,41608,76371,140944,261752,484968,904799,1689477,3160113,5928904
%N A095017 Number of lesser twin primes (A001359) in range ]2^n,2^(n+1)].
%Y A095017 Cf. A095016, A036378.
%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), May 28 2004

%I A095018
%S A095018 0,0,0,0,2,0,4,0,17,0,28,0,189,0,531,0,1990,0,5747,0,23902,0,76658,0,291478,0,982793,0,3677580,0,13214719
%N A095018 Number of binarily balanced primes (A066196) in range ]2^n,2^(n+1)].
%Y A095018 Cf. A095005-A095006.
%K A095018 nonn
%O A095018 1,5
%A A095018 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095019
%S A095019 0,0,0,1,0,3,3,11,10,40,52,130,154,482,649,1756,2483,6479,9640,24022,34812,89306,136739,335115,510833,1265350,1982321,4781514,7508064,18079040,28833595
%N A095019 Number of zero-bit dominant primes (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095019 Cf. A095018.
%K A095019 nonn
%O A095019 1,6
%A A095019 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095020
%S A095020 1,2,2,4,5,10,16,32,48,97,175,334,529,1130,1850,3953,6276,13911,23248,49564,81622,178910,300311,650703,1091809,2380394,4062176,8780393,15021634,32618497,56134342
%N A095020 Number of one-bit dominant primes (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095020 Cf. A095018.
%K A095020 nonn
%O A095020 1,2
%A A095020 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095052
%S A095052 0,0,0,1,0,3,0,10,0,25,0,78,0,283,0,906,0,3044,0,10920,0,37920,0,135182,0,487555,0,1764216,0,6415902,0
%N A095052 Number of primes with #0-bits = 1+#1-bits (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095052 Cf. A095018.
%K A095052 nonn
%O A095052 1,6
%A A095052 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095053
%S A095053 0,1,0,1,0,5,0,11,0,28,0,105,0,362,0,1093,0,3659,0,13001,0,45171,0,159510,0,563833,0,2008295,0,7333827,0
%N A095053 Number of primes with #1-bits = 1+#0-bits (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095053 Cf. A095018.
%K A095053 nonn
%O A095053 1,6
%A A095053 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095054
%S A095054 0,0,0,0,0,0,3,1,10,15,52,52,154,199,649,850,2483,3435,9640,13102,34812,51386,136739,199933,510833,777795,1982321,3017298,7508064,11663138,28833595
%N A095054 Number of primes with #0-bits > 1+#1-bits (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095054 Cf. A095018.
%K A095054 nonn
%O A095054 1,7
%A A095054 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095055
%S A095055 1,1,2,3,5,5,16,21,48,69,175,229,529,768,1850,2860,6276,10252,23248,36563,81622,133739,300311,491193,1091809,1816561,4062176,6772098,15021634,25284670,56134342
%N A095055 Number of primes with #1-bits > 1+#0-bits (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095055 Cf. A095018.
%K A095055 nonn
%O A095055 1,3
%A A095055 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 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
%N A095056 Number of primes with three 1-bits (A081091) in range ]2^n,2^(n+1)].
%Y A095056 Cf. A095018.
%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), May 28 2004

%I A095057
%S A095057 0,0,0,2,2,5,4,10,6,13,11,9,16,16,18,25,15,19,15,37,17,37,29,29,32,40,23,49,31,51,39
%N A095057 Number of primes with four 1-bits (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095057 Cf. A095018.
%K A095057 nonn
%O A095057 1,4
%A A095057 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 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
%N A095058 Number of primes with a single 0-bit (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095058 Cf. A095018.
%K A095058 nonn
%O A095058 1,3
%A A095058 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095059
%S A095059 0,0,0,1,2,4,0,9,5,14,4,16,9,18,0,21,21,21,7,41,22,31,5,37,20,33,14,37,45,47,0
%N A095059 Number of primes with two 0-bits (A0xxxxx) in range ]2^n,2^(n+1)].
%Y A095059 Cf. A095018.
%K A095059 nonn
%O A095059 1,5
%A A095059 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095021
%S A095021 0,0,1,1,2,2,7,9,19,33,64,115,216,402,754,1434,2669,5116,9651,18382,35064,67056,128394,246349,473469,911468,1757069,3389718,6551877,12674065,24546590
%N A095021 Number of 5k+1 primes (A030430) in range ]2^n,2^(n+1)].
%Y A095021 Cf. A036378.
%K A095021 nonn
%O A095021 1,5
%A A095021 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095022
%S A095022 0,1,0,1,2,4,5,11,22,33,65,117,220,404,762,1422,2693,5123,9634,18409,35112,67061,128302,246706,473477,911557,1756669,3390509,6552186,12674857,24545491
%N A095022 Number of 5k+2 primes (A030432) in range ]2^n,2^(n+1)].
%Y A095022 Cf. A036378.
%K A095022 nonn
%O A095022 1,5
%A A095022 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095023
%S A095023 1,0,1,1,2,4,5,11,18,36,63,117,220,407,760,1435,2682,5074,9683,18392,35113,67054,128503,246433,473717,911310,1756933,3390711,6551833,12673497,24546404
%N A095023 Number of 5k+3 primes (A030431) in range ]2^n,2^(n+1)].
%Y A095023 Cf. A036378.
%K A095023 nonn
%O A095023 1,5
%A A095023 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004

%I A095024
%S A095024 0,0,0,2,1,3,6,12,16,35,63,115,216,399,754,1418,2705,5077,9667,18403,35047,67045,128509,246330,473457,911409,1756619,3390969,6551382,12675118,24544171
%N A095024 Number of 5k+4 primes (A030433) in range ]2^n,2^(n+1)].
%Y A095024 Cf. A036378.
%K A095024 nonn
%O A095024 1,4
%A A095024 Labos E. (labos(AT)ana1.sote.hu) & Antti Karttunen (his-firstname.his-surname(AT)iki.fi), May 28 2004