%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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095765 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095765 nonn
%O A095765 1,4
%A A095765 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095766 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095766 nonn
%O A095766 1,4
%A A095766 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 2004

%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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095741 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095741 nonn
%O A095741 1,1
%A A095741 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095743 nonn
%O A095743 1,1
%A A095743 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095753 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095753 nonn
%O A095753 1,3
%A A095753 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095744 nonn
%O A095744 1,1
%A A095744 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095754 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095754 nonn
%O A095754 1,5
%A A095754 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095745 nonn
%O A095745 1,1
%A A095745 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095755 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095755 nonn
%O A095755 1,7
%A A095755 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095746 nonn
%O A095746 1,1
%A A095746 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095756 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095756 nonn
%O A095756 1,9
%A A095756 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095747 nonn
%O A095747 1,1
%A A095747 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095757 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095757 nonn
%O A095757 1,2
%A A095757 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095760 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095760 nonn
%O A095760 1,2
%A A095760 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095748 nonn
%O A095748 1,1
%A A095748 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095758 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%K A095758 nonn
%O A095758 1,4
%A A095758 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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 odd primes are all palindromes, 4-bit primes need on average just a one-bit flip to become palindromes, etc.
%C A095742 Ratio (a(n)/A036378(n))/f(n), where f(n) is (n-1)/4 if n is odd, and (n-2)/4 if n is even (i.e. it gives the expected assymetricity for all odd numbers in range [2^n,2^(n+1)]) converges as: 1, 1, 2, 1.2, 1.285714, 1.230769, 1.014493, 1.069767, 0.986667, 0.989051, 0.985098, 1.006034, 1.004969, 0.998759, 0.999246, 1.00508, 0.998418, 1.000233, 1.002102, 1.000535, 0.999575, 0.999758, 1.000064, 1.000084, 0.999727, 0.999975, 0.999912, 1.000105, 1.00004, 1.000046, 0.999964, 0.999985, 0.999991, ...
%Y A095742 Cf. A095298, A095732 (sums of similar assymetricity measures for Zeckendorf-expansion), A095753.
%H A095742 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095742 nonn
%O A095742 1,3
%A A095742 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095730 nonn
%O A095730 1,1
%A A095730 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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.
%Y A095731 A095732, A095741.
%H A095731 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095731 nonn
%O A095731 1,16
%A A095731 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 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
%Y A095732 Cf. A095730, A095731, A095742 (sums of similar assymetricity measures for binary-expansion).
%H A095732 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095732 nonn
%O A095732 1,4
%A A095732 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 2004