Cheers,

44 new sequences, in ranges A095280-A095298, A095312-A095336 & A095353-A095354.

%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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095280 nonn
%O A095280 1,1
%A A095280 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095290 <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 A095290 nonn
%O A095290 1,4
%A A095290 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095281 nonn
%O A095281 1,1
%A A095281 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095291
%S A095291 0,2,1,2,2,5,9,13,35,51,93,175,331,595,1149,2182,4097,7749,14780,
%T A095291 28131,53583,102372,196345,375876,722743,1392156,2684022,5180823,
%U A095291 10008419,19368226,37499404,72698062,141064116
%N A095291 Number of Upper Wythoff Primes (A095281) in range ]2^n,2^(n+1)].
%C A095291 As expected, the ratio of a(n)/A036378(n) seems to approach 1-((sqrt(5)-1)/2) (= 0.381966011250...): 0, 1, 0.5, 0.4, 0.285714, 0.384615, 0.391304, 0.302326, 0.466667, 0.372263, 0.364706, 0.377155, 0.379587, 0.369107, 0.379208, 0.382204, 0.381152, 0.380039, 0.382555, 0.382287, 0.381819, 0.381677, 0.382211, 0.381283, 0.381572, 0.381858, 0.381943, 0.382013, 0.381895, 0.382035, 0.381935, 0.381947, 0.381953
%C A095291 Also expected, the ratio a(n)/A095061(n) seems to approach 1: 1, 0, 0, 1, 0.5, 1.25, 1.28571, 0.72222, 1.4, 0.94444, 0.88571, 0.98315, 0.99699, 0.93407, 0.98627, 0.99453, 0.98462, 0.9973, 0.99865, 1.0011, 1.00108, 0.99979, 1.00208, 0.99622, 0.99835, 1.00039, 0.99973, 1.00046, 0.99983, 1.00031, 0.99994, 0.99994, 1.00001
%Y A095291 a(n) = A036378(n)-A095290(n). Cf. A095061, A095290.
%H A095291 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095291 <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 A095291 nonn
%O A095291 1,2
%A A095291 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095282 nonn
%O A095282 1,1
%A A095282 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095292 <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 A095292 nonn
%O A095292 1,5
%A A095292 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095283 nonn
%O A095283 1,1
%A A095283 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095293
%S A095293 0,2,1,4,4,9,14,29,52,90,167,312,577,1072,2026,3776,7177,13585,25726,
%T A095293 49125,93569,178735,342381,657180,1262818,2430501,4684999,9040931,
%U A095293 17470670,33798206,65455531,126889351,246216909
%N A095293 Number of A095283-primes in range ]2^n,2^(n+1)].
%C A095293 As expected, the ratio a(n)/A095292(n) seems to approach 2: 0, 0, 1, 4, 1.33333, 2.25, 1.55556, 2.07143, 2.26087, 1.91489, 1.89773, 2.05263, 1.95593, 1.98519, 2.01793, 1.95344, 2.00924, 1.99633, 1.99287, 2.0083, 2.00075, 1.99746, 1.99841, 1.99971, 2.00034, 2.00001, 2.00018, 1.99977, 1.99971, 1.99997, 2.00004, 1.99995, 2.00003
%Y A095293 a(n) = A036378(n)-A095292(n). Cf. A095005.
%H A095293 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095293 <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 A095293 nonn
%O A095293 1,2
%A A095293 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095320
%S A095320 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095320 89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,
%U A095320 179,181,191,193,197,199,211,223,227,229,233,239,241,251,263,269
%N A095320 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 3.
%C A095320 Differs from primes (A000040) first time at n=55, where a(55)=263, while A000040(55)=257, as 257 whose binary expansion is 100000001, with 2 1-bits and 7 0-bits is the first prime excluded from this sequence. Note that 129 (10000001 in binary, 2 1-bits and 6 0-bits) is not prime.
%Y A095320 Complement of A095321 in A000040. Subset: A095316. Cf. A095330.
%H A095320 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 A095320 nonn
%O A095320 1,1
%A A095320 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095330
%S A095330 1,2,2,5,7,13,23,42,71,122,241,412,789,1413,2770,4859,9545,16955,
%T A095330 34039,60484,121241,216830,441223,785885,1597803,2867949,5874665,
%U A095330 10544609,21636090,39034399,80414166,145210901,299284792
%N A095330 Number of A095320-primes in range ]2^n,2^(n+1)].
%C A095330 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 1, 1, 0.976744, 0.946667, 0.890511, 0.945098, 0.887931, 0.904817, 0.876551, 0.914191, 0.851112, 0.88799, 0.831535, 0.881041, 0.82195, 0.863934, 0.808416, 0.858898, 0.797191, 0.84356, 0.786657, 0.835979, 0.777517, 0.825576, 0.769947, 0.819026, 0.76292, 0.81036
%Y A095330 a(n) = A036378(n)-A095331(n).
%H A095330 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095330 <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 A095330 nonn
%O A095330 1,2
%A A095330 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095321
%S A095321 257,521,577,641,769,1031,1033,1049,1061,1091,1093,1097,1153,1217,
%T A095321 1283,1289,1297,1409,1553,1601,2053,2069,2081,2083,2089,2113,2129,
%U A095321 2179,2309,2593,2689,3089,3137,3329,4099,4111,4129,4133,4139,4153
%N A095321 Primes in whose binary expansion the number of 1-bits is <= number of 0-bits minus 3.
%Y A095321 Complement of A095320 in A000040. Subset of A095317. Cf. also A095331.
%H A095321 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095321 nonn
%O A095321 1,1
%A A095321 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095331
%S A095331 0,0,0,0,0,0,0,1,4,15,14,52,83,199,260,850,1204,3435,4596,13102,19095,
%T A095331 51386,72485,199933,296317,777795,1152625,3017298,4571188,11663138,
%U A095331 17768490,45124684,70038513
%N A095331 Number of A095321-primes in range ]2^n,2^(n+1)].
%C A095331 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0, 0, 0.023256, 0.053333, 0.109489, 0.054902, 0.112069, 0.095183, 0.123449, 0.085809, 0.148888, 0.11201, 0.168465, 0.118959, 0.17805, 0.136066, 0.191584, 0.141102, 0.202809, 0.15644, 0.213343, 0.164021, 0.222483, 0.174424, 0.230053, 0.180974, 0.23708, 0.18964
%Y A095331 a(n) = A036378(n)-A095330(n).
%H A095331 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095331 <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 A095331 nonn
%O A095331 1,9
%A A095331 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095316
%S A095316 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095316 89,97,101,103,107,109,113,127,139,149,151,157,163,167,173,179,181,
%U A095316 191,197,199,211,223,227,229,233,239,241,251,263,269,271,277,281
%N A095316 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 2.
%C A095316 Differs from primes (A000040) first time at n=32, where a(32)=139, while A000040(32)=131, as 131 whose binary expansion is 10000011, with 3 1-bits and 5 0-bits is the first prime excluded from this sequence.
%Y A095316 Complement of A095317 in A000040. Subset of A095320. Subset: A095074. Cf. also A095326.
%H A095316 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095316 nonn
%O A095316 1,1
%A A095316 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095326
%S A095326 1,2,2,5,7,13,20,42,65,122,203,412,718,1413,2381,4859,8266,16955,
%T A095326 28995,60484,105524,216830,376969,785885,1383287,2867949,5044969,
%U A095326 10544609,18699214,39034399,69349061,145210901,259051224
%N A095326 Number of A095316-primes in range ]2^n,2^(n+1)].
%C A095326 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 1, 0.869565, 0.976744, 0.866667, 0.890511, 0.796078, 0.887931, 0.823394, 0.876551, 0.785809, 0.851112, 0.769002, 0.831535, 0.750485, 0.82195, 0.751938, 0.808416, 0.73382, 0.797191, 0.730306, 0.786657, 0.717911, 0.777517, 0.713512, 0.769947, 0.706327, 0.76292, 0.701421
%Y A095326 a(n) = A036378(n)-A095327(n).
%H A095326 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095326 <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 A095326 nonn
%O A095326 1,2
%A A095326 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095317
%S A095317 131,137,193,257,521,523,547,577,593,641,643,673,769,773,1031,1033,
%T A095317 1049,1061,1091,1093,1097,1153,1217,1283,1289,1297,1409,1553,1601,
%U A095317 2053,2063,2069,2081,2083,2087,2089,2099,2113,2129,2131,2137,2153
%N A095317 Primes in whose binary expansion the number of 1-bits is <= number of 0-bits minus 2.
%Y A095317 Complement of A095316 in A000040. Subset: A095321. Subset of A095071. Cf. also A095327.
%H A095317 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095317 nonn
%O A095317 1,1
%A A095317 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 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: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095327 <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 A095327 nonn
%O A095327 1,7
%A A095327 Antti Karttunen (his-firstname.his-surname(AT)iki.fi)
%C A095327 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0, 0.130435, 0.023256, 0.133333, 0.109489, 0.203922, 0.112069, 0.176606, 0.123449, 0.214191, 0.148888, 0.230998, 0.168465, 0.249515, 0.17805, 0.248062, 0.191584, 0.26618, 0.202809, 0.269694, 0.213343, 0.282089, 0.222483, 0.286488, 0.230053, 0.293673, 0.23708, 0.298579, Jun 04 2004









%I A095286
%S A095286 3,7,11,13,23,29,31,43,47,53,59,61,79,103,107,109,127,151,157,167,
%T A095286 173,179,181,191,199,211,223,227,229,233,239,241,251,311,317,347,
%U A095286 349,359,367,373,379,383,431,439,443,461,463,467,479,487,491,499
%N A095286 Primes in whose binary expansion the number of 1-bits is > 1 + number of 0-bits.
%Y A095286 Complement of A095287 in A000040. Subset of A095070. Subset: A095314. Cf. also A095296.
%H A095286 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095286 nonn
%O A095286 1,1
%A A095286 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095296
%S A095296 1,1,2,3,5,5,16,21,48,69,175,229,529,768,1850,2860,6276,10252,23248,
%T A095296 36563,81622,133739,300311,491193,1091809,1816561,4062176,6772098,
%U A095296 15021634,25284670,56134342,94895078,209889612
%N A095296 Number of A095286-primes in range ]2^n,2^(n+1)].
%C A095296 Ratios a(n)/A036378(n) converge as: 1, 0.5, 1, 0.6, 0.714286, 0.384615, 0.695652, 0.488372, 0.64, 0.50365, 0.686275, 0.493534, 0.606651, 0.476427, 0.610561, 0.500963, 0.583868, 0.502795, 0.601734, 0.496874, 0.581618, 0.498624, 0.584595, 0.498259, 0.57642, 0.498269, 0.578057, 0.499347, 0.573186, 0.498736, 0.571734, 0.498567, 0.568309
%C A095296 Ratios a(n)/A095335(n) converge as: 1, 1, 1, 1.5, 1.25, 0.625, 0.842105, 0.954545, 1.116279, 1.014706, 1.100629, 0.974468, 0.985102, 0.909953, 0.966562, 1.003861, 0.984008, 1.011245, 1.00445, 0.987575, 0.991822, 0.994512, 0.988408, 0.993061, 0.99389, 0.9931, 0.99673, 0.997392, 0.997286, 0.994955, 0.995265, 0.994285, 0.996248
%Y A095296 a(n) = A036378(n)-A095297(n). Cf. A095298.
%H A095296 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095296 <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 A095296 nonn
%O A095296 1,3
%A A095296 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095287
%S A095287 2,5,17,19,37,41,67,71,73,83,89,97,101,113,131,137,139,149,163,193,
%T A095287 197,257,263,269,271,277,281,283,293,307,313,331,337,353,389,397,
%U A095287 401,409,419,421,433,449,457,521,523,541,547,557,563,569,577,587
%N A095287 Primes in whose binary expansion the number of 1-bits is <= 1 + number of 0-bits.
%Y A095287 Complement of A095286 in A000040. Subset: A095075. Subset of A095315. Cf. also A095297.
%H A095287 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095287 nonn
%O A095287 1,1
%A A095287 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095297
%S A095297 0,1,0,2,2,8,7,22,27,68,80,235,343,844,1180,2849,4473,10138,15387,
%T A095297 37023,58714,134477,213397,494625,802311,1829183,2965114,6789809,
%U A095297 11185644,25412867,42048314,95440507,159433693
%N A095297 Number of A095287-primes in range ]2^n,2^(n+1)].
%C A095297 Ratios a(n)/A036378(n) converge as: 0, 0.5, 0, 0.4, 0.285714, 0.615385, 0.304348, 0.511628, 0.36, 0.49635, 0.313725, 0.506466, 0.393349, 0.523573, 0.389439, 0.499037, 0.416132, 0.497205, 0.398266, 0.503126, 0.418382, 0.501376, 0.415405, 0.501741, 0.42358, 0.501731, 0.421943, 0.500653, 0.426814, 0.501264, 0.428266, 0.501433, 0.431691
%C A095297 Ratios a(n)/A095334(n) converge as: 1, 1, 1, 0.666667, 0.666667, 1.6, 1.75, 1.047619, 0.84375, 0.985507, 0.833333, 1.026201,1.023881, 1.098958, 1.057348, 0.996154, 1.023336, 0.98888, 0.993351,1.012581, 1.011595, 1.005518, 1.016781, 1.006987, 1.008436, 1.006948,1.004514, 1.002615, 1.003668, 1.00507, 1.006392, 1.005748, 1.004982
%Y A095297 a(n) = A036378(n)-A095296(n). Cf. A095298.
%H A095297 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095297 <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 A095297 nonn
%O A095297 1,4
%A A095297 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095314
%S A095314 7,23,29,31,47,59,61,79,103,107,109,127,191,223,239,251,311,317,347,
%T A095314 349,359,367,373,379,383,431,439,443,461,463,467,479,487,491,499,
%U A095314 503,509,607,631,701,719,727,733,743,751,757,761,823,827,829,859
%N A095314 Primes in whose binary expansion the number of 1-bits is > 2 + number of 0-bits.
%Y A095314 Complement of A095315 in A000040. Subset of A095286. Subset: A095318. Cf. also A095334.
%H A095314 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095314 nonn
%O A095314 1,1
%A A095314 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095334
%S A095334 0,1,0,3,3,5,4,21,32,69,96,229,335,768,1116,2860,4371,10252,15490,
%T A095334 36563,58041,133739,209875,491193,795599,1816561,2951789,6772098,
%U A095334 11144763,25284670,41781268,94895078,158643268
%N A095334 Number of A095314-primes in range ]2^n,2^(n+1)].
%C A095334 Ratios a(n)/A036378(n) converge as: 0, 0.5, 0, 0.6, 0.428571, 0.384615, 0.173913, 0.488372, 0.426667, 0.50365, 0.376471, 0.493534, 0.384174, 0.476427, 0.368317, 0.500963, 0.406642, 0.502795, 0.400932, 0.496874, 0.413586, 0.498624, 0.408549, 0.498259, 0.420036, 0.498269, 0.420047, 0.499347, 0.425255, 0.498736, 0.425546, 0.498567, 0.429551
%C A095334 Ratios a(n)/A095297(n) converge as: 1, 1, 1, 1.5, 1.5, 0.625, 0.571429, 0.954545, 1.185185, 1.014706, 1.2, 0.974468, 0.976676, 0.909953, 0.945763, 1.003861, 0.977197, 1.011245, 1.006694, 0.987575, 0.988538, 0.994512, 0.983496, 0.993061, 0.991634, 0.9931, 0.995506, 0.997392, 0.996345, 0.994955, 0.993649, 0.994285, 0.995042
%Y A095334 a(n) = A036378(n)-A095335(n). Cf. A095298.
%H A095334 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095334 <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 A095334 nonn
%O A095334 1,4
%A A095334 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095315
%S A095315 2,3,5,11,13,17,19,37,41,43,53,67,71,73,83,89,97,101,113,131,137,
%T A095315 139,149,151,157,163,167,173,179,181,193,197,199,211,227,229,233,
%U A095315 241,257,263,269,271,277,281,283,293,307,313,331,337,353,389,397
%N A095315 Primes in whose binary expansion the number of 1-bits is <= 2 + number of 0-bits.
%Y A095315 Complement of A095314 in A000040. Subset: A095287. Subset of A095319. Cf. also A095335.
%H A095315 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095315 nonn
%O A095315 1,1
%A A095315 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095335
%S A095335 1,1,2,2,4,8,19,22,43,68,159,235,537,844,1914,2849,6378,10138,23145,
%T A095335 37023,82295,134477,303833,494625,1098521,1829183,4075501,6789809,
%U A095335 15062515,25412867,56401388,95440507,210680037
%N A095335 Number of A09515-primes in range ]2^n,2^(n+1)].
%C A095335 Ratios a(n)/A036378(n) converge as: 1, 0.5, 1, 0.4, 0.571429, 0.615385, 0.826087, 0.511628, 0.573333, 0.49635, 0.623529, 0.506466, 0.615826, 0.523573, 0.631683, 0.499037, 0.593358, 0.497205, 0.599068, 0.503126, 0.586414, 0.501376, 0.591451, 0.501741, 0.579964, 0.501731, 0.579953, 0.500653, 0.574745, 0.501264, 0.574454, 0.501433, 0.570449
%C A095335 Ratios a(n)/A095296(n) converge as: 1, 1, 1, 0.666667, 0.8,1.6, 1.1875, 1.047619, 0.895833, 0.985507, 0.908571, 1.026201,1.015123, 1.098958, 1.034595, 0.996154, 1.016252, 0.98888, 0.99557,1.012581, 1.008245, 1.005518, 1.011728, 1.006987, 1.006148, 1.006948,1.00328, 1.002615, 1.002721, 1.00507, 1.004757, 1.005748, 1.003766
%Y A095335 a(n) = A036378(n)-A095334(n).
%H A095335 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095335 <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 A095335 nonn
%O A095335 1,3
%A A095335 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095318
%S A095318 31,47,59,61,127,191,223,239,251,367,379,383,431,439,443,463,479,
%T A095318 487,491,499,503,509,607,631,701,719,727,733,743,751,757,761,823,
%U A095318 827,829,859,863,877,883,887,911,919,941,947,953,967,971,983,991
%N A095318 Primes in whose binary expansion the number of 1-bits is > 3 + number of 0-bits.
%Y A095318 Complement of A095319 in A000040. Subset of A095314. Subset: A095322. Cf. also A095328.
%H A095318 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095318 nonn
%O A095318 1,1
%A A095318 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095328
%S A095328 0,0,0,1,3,1,4,13,32,35,96,124,335,466,1116,1717,4371,6380,15490,
%T A095328 23904,58041,88200,209875,331769,795599,1258386,2951789,4741344,11144763,
%U A095328 17964801,41781268,68371012,158643268
%N A095328 Number of A095318-primes in range ]2^n,2^(n+1)].
%C A095328 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0.428571, 0.076923, 0.173913, 0.302326, 0.426667, 0.255474, 0.376471, 0.267241, 0.384174, 0.289082, 0.368317, 0.300753, 0.406642, 0.312898, 0.400932, 0.324844, 0.413586, 0.328839, 0.408549, 0.336542, 0.420036, 0.345166, 0.420047, 0.349607, 0.425255, 0.354353, 0.425546, 0.359213, 0.429551
%C A095328 Ratios a(n)/A095055(n) converge as: 1, 1, 1, 1, 1.5, 0.333333, 0.571429, 1.181818, 1.185185, 0.875, 1.2, 0.953846, 0.976676, 0.966805, 0.945763, 0.97779, 0.977197, 0.98472, 1.006694, 0.995088, 0.988538, 0.987616, 0.983496, 0.990015, 0.991634, 0.994496, 0.995506, 0.991599, 0.996345, 0.993681, 0.993649, 0.995067, 0.995042
%Y A095328 a(n) = A036378(n)-A095329(n).
%H A095328 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095328 <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 A095328 nonn
%O A095328 1,5
%A A095328 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095319
%S A095319 2,3,5,7,11,13,17,19,23,29,37,41,43,53,67,71,73,79,83,89,97,101,103,
%T A095319 107,109,113,131,137,139,149,151,157,163,167,173,179,181,193,197,
%U A095319 199,211,227,229,233,241,257,263,269,271,277,281,283,293,307,311
%N A095319 Primes in whose binary expansion the number of 1-bits is <= 3 + number of 0-bits.
%Y A095319 Complement of A095318 in A000040. Subset of A095323, subset: A095315. A095329.
%H A095319 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095319 nonn
%O A095319 1,1
%A A095319 Antti Karttunen (his-firstname.his-surname(AT)iki.fi)
%C A095319 Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with 5 1-bits and no 0-bits is the first prime excluded from this sequence., Jun 04 2004

%I A095329
%S A095329 1,2,2,4,4,12,19,30,43,102,159,340,537,1146,1914,3992,6378,14010,
%T A095329 23145,49682,82295,180016,303833,654049,1098521,2387358,4075501,8820563,
%U A095329 15062515,32732736,56401388,121964573,210680037
%N A095329 Number of A095319-primes in range ]2^n,2^(n+1)].
%C A095329 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 0.571429, 0.923077, 0.826087, 0.697674, 0.573333, 0.744526, 0.623529, 0.732759, 0.615826, 0.710918, 0.631683, 0.699247, 0.593358, 0.687102, 0.599068, 0.675156, 0.586414, 0.671161, 0.591451, 0.663458, 0.579964, 0.654834, 0.579953, 0.650393, 0.574745, 0.645647, 0.574454, 0.640787, 0.570449
%C A095329 Ratios a(n)/A095020(n) converge as: 1, 1, 1, 1, 0.8, 1.2,1.1875, 0.9375, 0.895833, 1.051546, 0.908571, 1.017964, 1.015123,1.014159, 1.034595, 1.009866, 1.016252, 1.007117, 0.99557, 1.002381,1.008245, 1.006182, 1.011728, 1.005142, 1.006148, 1.002926, 1.00328,1.004575, 1.002721, 1.003502, 1.004757, 1.002787, 1.003766
%Y A095329 a(n) = A036378(n)-A095328(n).
%H A095329 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095329 <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 A095329 nonn
%O A095329 1,2
%A A095329 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095322
%S A095322 31,127,191,223,239,251,367,379,383,431,439,443,463,479,487,491,499,
%T A095322 503,509,751,863,887,983,991,1013,1019,1021,1151,1277,1279,1399,1439,
%U A095322 1471,1487,1499,1511,1523,1531,1663,1723,1759,1783,1787,1789,1823
%N A095322 Primes in whose binary expansion the number of 1-bits is > 4 + number of 0-bits.
%Y A095322 Complement of A095323 in A000040. Subset of A095318. Subset: A095284. Cf. also A095324.
%H A095322 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095322 nonn
%O A095322 1,1
%A A095322 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095324
%S A095324 0,0,0,1,0,1,4,13,8,35,44,124,150,466,701,1717,2326,6380,9354,23904,
%T A095324 34443,88200,134780,331769,508200,1258386,1957824,4741344,7424464,
%U A095324 17964801,28737086,68371012,109643089
%N A095324 Number of A095322-primes in range ]2^n,2^(n+1)].
%C A095324 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0.2, 0, 0.076923, 0.173913, 0.302326, 0.106667, 0.255474, 0.172549, 0.267241, 0.172018, 0.289082, 0.231353, 0.300753, 0.216392, 0.312898, 0.242112, 0.324844, 0.245432, 0.328839, 0.262367, 0.336542, 0.268304, 0.345166, 0.278603, 0.349607, 0.283298, 0.354353, 0.29269, 0.359213, 0.296876
%C A095324 Ratios a(n)/A095019(n) converge as: 1, 1, 1, 1, 1, 0.333333, 1.333333, 1.181818, 0.8, 0.875, 0.846154, 0.953846, 0.974026, 0.966805, 1.080123, 0.97779, 0.93677, 0.98472, 0.970332, 0.995088, 0.9894, 0.987616, 0.985673, 0.990015, 0.994846, 0.994496, 0.987642, 0.991599, 0.988865, 0.993681, 0.996653, 0.995067, 0.994296
%Y A095324 a(n) = A036378(n)-A095325(n).
%H A095324 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095324 <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 A095324 nonn
%O A095324 1,7
%A A095324 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095323
%S A095323 2,3,5,7,11,13,17,19,23,29,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T A095323 97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,181,
%U A095323 193,197,199,211,227,229,233,241,257,263,269,271,277,281,283,293
%N A095323 Primes in whose binary expansion the number of 1-bits is <= 4 + number of 0-bits.
%C A095323 Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with 5 1-bits and no 0-bits is the first prime excluded from this sequence. Note that 15 (1111 in binary) is not prime.
%Y A095323 Complement of A095322 in A000040. Subset of A095285. subset: A095319. A095325.
%H A095323 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095323 nonn
%O A095323 1,1
%A A095323 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095325
%S A095325 1,2,2,4,7,12,19,30,67,102,211,340,722,1146,2329,3992,8423,14010,
%T A095325 29281,49682,105893,180016,378928,654049,1385920,2387358,5069466,
%U A095325 8820563,18782814,32732736,69445570,121964573,259680216
%N A095325 Number of A095323-primes in range ]2^n,2^(n+1)].
%C A095325 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 0.8, 1, 0.923077, 0.826087, 0.697674, 0.893333, 0.744526, 0.827451, 0.732759, 0.827982, 0.710918, 0.768647, 0.699247, 0.783608, 0.687102, 0.757888, 0.675156, 0.754568, 0.671161, 0.737633, 0.663458, 0.731696, 0.654834, 0.721397, 0.650393, 0.716702, 0.645647, 0.70731, 0.640787, 0.703124
%C A095325 Ratios a(n)/A095054(n) converge as: 1, 1, 1, 1, 1, 1.2, 0.95, 0.9375, 1.030769, 1.051546, 1.039409, 1.017964, 1.005571,1.014159, 0.97816, 1.009866, 1.018993, 1.007117, 1.009864, 1.002381,1.003497, 1.006182, 1.005197, 1.005142, 1.001903, 1.002926, 1.004856,1.004575, 1.004471, 1.003502, 1.001392, 1.002787, 1.002428
%Y A095325 a(n) = A036378(n)-A095324(n).
%H A095325 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095325 <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 A095325 nonn
%O A095325 1,2
%A A095325 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095284
%S A095284 127,191,223,239,251,383,479,503,509,751,863,887,983,991,1013,1019,
%T A095284 1021,1279,1471,1531,1663,1759,1783,1787,1789,1951,1979,1999,2011,
%U A095284 2027,2029,2039,2543,2551,2557,2687,2879,2927,2939,2999,3023,3037
%N A095284 Primes in whose binary expansion the number of 1-bits is > 5 + number of 0-bits.
%Y A095284 Complement of A095285 in A000040. Subset of A095322. Subset: A095312.Cf. also A095286, A095294.
%H A095284 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095284 nonn
%O A095284 1,1
%A A095284 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095294
%S A095294 0,0,0,0,0,1,4,4,8,15,44,47,150,236,701,863,2326,3298,9354,12933,
%T A095294 34443,51300,134780,199410,508200,769127,1957824,2978179,7424464,
%U A095294 11590386,28737086,44867556,109643089
%N A095294 Number of A095284-primes in range ]2^n,2^(n+1)].
%C A095294 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0.076923, 0.173913, 0.093023, 0.106667, 0.109489, 0.172549, 0.101293, 0.172018, 0.146402, 0.231353, 0.151165, 0.216392, 0.161746, 0.242112, 0.175754, 0.245432, 0.191264, 0.262367, 0.202279, 0.268304, 0.210966, 0.278603, 0.219599, 0.283298, 0.228618, 0.29269, 0.235729, 0.296876
%C A095294 Ratios a(n)/A095327(n) converge as: 1, 1, 1, 1, 1, 0,1.333333, 4., 0.8, 1, 0.846154, 0.903846, 0.974026, 1.18593, 1.080123,1.015294, 0.93677, 0.960116, 0.970332, 0.987101, 0.9894, 0.998326, 0.985673, 0.997384, 0.994846, 0.988856, 0.987642, 0.987035, 0.988865, 0.993762, 0.996653, 0.994302, 0.994296
%Y A095294 a(n) = A036378(n)-A095295(n). Cf. also A095329, A095052, A095053
%H A095294 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095294 <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 A095294 nonn
%O A095294 1,7
%A A095294 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095285
%S A095285 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095285 89,97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,
%U A095285 181,193,197,199,211,227,229,233,241,257,263,269,271,277,281,283
%N A095285 Primes in whose binary expansion the number of 1-bits is <= 5 + number of 0-bits.
%C A095285 Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence. Note that 63 (111111 in binary) is not prime.
%Y A095285 Complement of A095284 in A000040. Subset: A095323. Subset of A095313, from which it differs first time at n=42, where a(42)=193 (11000001 in binary) while A095313(42)=191 (10111111 in binary). Cf. also A095286, A095295.
%H A095285 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095285 nonn
%O A095285 1,1
%A A095285 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095295
%S A095295 1,2,2,5,7,12,19,39,67,122,211,417,722,1376,2329,4846,8423,17092,
%T A095295 29281,60653,105893,216916,378928,786408,1385920,2876617,5069466,
%U A095295 10583728,18782814,39107151,69445570,145468029,259680216
%N A095295 Number of A095285-primes in range ]2^n,2^(n+1)].
%C A095295 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 0.923077, 0.826087, 0.906977, 0.893333, 0.890511, 0.827451, 0.898707, 0.827982, 0.853598, 0.768647, 0.848835, 0.783608, 0.838254, 0.757888, 0.824246, 0.754568, 0.808736, 0.737633, 0.797721, 0.731696, 0.789034, 0.721397, 0.780401, 0.716702, 0.771382, 0.70731, 0.764271, 0.703124
%C A095295 Ratios a(n)/A095326(n) converge as: 1, 1, 1, 1, 1, 0.923077, 0.95, 0.928571, 1.030769, 1, 1.039409, 1.012136, 1.005571, 0.973815, 0.97816, 0.997325, 1.018993, 1.00808, 1.009864, 1.002794,1.003497, 1.000397, 1.005197, 1.000665, 1.001903, 1.003022, 1.004856,1.00371, 1.004471, 1.001864, 1.001392, 1.001771, 1.002428
%Y A095295 a(n) = A036378(n)-A095294(n). A095052, A095053
%H A095295 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095295 <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 A095295 nonn
%O A095295 1,2
%A A095295 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095312
%S A095312 127,383,479,503,509,991,1019,1021,1279,1471,1531,1663,1759,1783,
%T A095312 1787,1789,1951,1979,1999,2011,2027,2029,2039,3067,3581,3583,3823,
%U A095312 3967,4027,4079,4091,4093,5087,5119,5503,5623,5879,6007,6011,6047
%N A095312 Primes in whose binary expansion the number of 1-bits is > 6 + number of 0-bits.
%Y A095312 Complement of A095313 in A000040. Subset of A095284. Cf. also A095332.
%H A095312 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095312 nonn
%O A095312 1,1
%A A095312 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095332
%S A095332 0,0,0,0,0,1,0,4,3,15,9,47,73,236,251,863,1180,3298,4284,12933,18598,
%T A095332 51300,73371,199410,292156,769127,1131645,2978179,4533090,11590386,
%U A095332 17623347,44867556,69537472
%N A095332 Number of A095312-primes in range ]2^n,2^(n+1)].
%C A095332 Ratios a(n)/A036378(n) converge as: 0, 0, 0, 0, 0, 0.076923, 0, 0.093023, 0.04, 0.109489, 0.035294, 0.101293, 0.083716, 0.146402, 0.082838, 0.151165, 0.109778, 0.161746, 0.110884, 0.175754, 0.132525, 0.191264, 0.142826, 0.202279, 0.154244, 0.210966, 0.161036, 0.219599, 0.172971, 0.228618, 0.179496, 0.235729, 0.188283
%C A095332 Ratios a(n)/A095331(n) converge as: 1, 1, 1, 1, 1, 0, 1,4, 0.75, 1, 0.642857, 0.903846, 0.879518, 1.18593, 0.965385,1.015294, 0.980066, 0.960116, 0.932115, 0.987101, 0.973972, 0.998326,1.012223, 0.997384, 0.985958, 0.988856, 0.981798, 0.987035, 0.991666, 0.993762, 0.991831, 0.994302, 0.992846
%Y A095332 a(n) = A036378(n)-A095333(n).
%H A095332 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095332 <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 A095332 nonn
%O A095332 1,8
%A A095332 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095313
%S A095313 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A095313 89,97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,
%U A095313 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269
%N A095313 Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.
%C A095313 Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence.
%Y A095313 Complement of A095312 in A000040. Subset: A095285, from which it differs first time at n=42, where a(42)=191 (10111111 in binary), while A095285(42)=193 (11000001 in binary).Cf. also A095333.
%H A095313 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095313 nonn
%O A095313 1,1
%A A095313 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095333
%S A095333 1,2,2,5,7,12,23,39,72,122,246,417,799,1376,2779,4846,9569,17092,
%T A095333 34351,60653,121738,216916,440337,786408,1601964,2876617,5895645,
%U A095333 10583728,21674188,39107151,80559309,145468029,299785833
%N A095333 Number of A095313-primes in range ]2^n,2^(n+1)].
%C A095333 Ratios a(n)/A036378(n) converge as: 1, 1, 1, 1, 1, 0.923077, 1, 0.906977, 0.96, 0.890511, 0.964706, 0.898707, 0.916284, 0.853598, 0.917162, 0.848835, 0.890222, 0.838254, 0.889116, 0.824246, 0.867475, 0.808736, 0.857174, 0.797721, 0.845756, 0.789034, 0.838964, 0.780401, 0.827029, 0.771382, 0.820504, 0.764271, 0.811717
%C A095333 Ratios a(n)/A095330(n) converge as: 1, 1, 1, 1, 1, 0.923077, 1, 0.928571, 1.014085, 1, 1.020747, 1.012136, 1.012674, 0.973815, 1.003249, 0.997325, 1.002514, 1.00808, 1.009166, 1.002794,1.004099, 1.000397, 0.997992, 1.000665, 1.002604, 1.003022, 1.003571,1.00371, 1.001761, 1.001864, 1.001805, 1.001771, 1.001674
%Y A095333 a(n) = A036378(n)-A095332(n).
%H A095333 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%H A095333 <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 A095333 nonn
%O A095333 1,2
%A A095333 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095298
%S A095298 0,1,2,8,15,30,67,154,302,611,1280,2546,5207,10447,21123,42783,85726,
%T A095298 173102,347243,698544,1401784,2813930,5644165,11328192,22712057,45538473,
%U A095298 91288241,182965151,366691833,734702678,1471976078,2948741819,5906481468
%N A095298 Sum of 1-bits between the most and least significant bits summed for all primes in range ]2^n,2^(n+1)].
%e A095298 a(1)=0, as only prime in range ]2,4] is 3, 11 in binary which has  no space between its most and least significant bits. a(2)=1, as in that range there are two primes 5 (101 in binary) and 7 (111 in binary) and summing their middle bits we get 1. a(3)=2, as there are again two primes, 11 (1011 in binary), and 13 (1101 in binary), and summing the bits in the middle we get total 2.
%C A095298 Ratio a(n)/A036378(n) (i.e. average number of 1-bits in range ]msb,lsb[ of primes p which 2^n < p < 2^(n+1)) grows as:  0, 0.5, 1, 1.6, 2.142857, 2.307692, 2.913043, 3.581395, 4.026667, 4.459854, 5.019608, 5.487069, 5.97133, 6.480769, 6.971287, 7.493957, 7.975254, 8.489554, 8.987783, 9.492893, 9.98877, 10.491283, 10.987107, 11.49116, 11.990823, 12.490859, 12.990533, 13.491108, 13.991985, 14.491881, 14.992221, 15.492331, 15.992713.
%C A095298 Ratio of that average compared to (n-1)/2 (the expected value of that same sum computed for all odd numbers in the same range) converges as: 1, 1, 1, 1.066667, 1.071429, 0.923077, 0.971014, 1.023256, 1.006667, 0.991079, 1.003922, 0.997649, 0.995222, 0.997041, 0.995898, 0.999194, 0.996907, 0.998771, 0.998643, 0.999252, 0.998877, 0.99917, 0.998828, 0.999231, 0.999235, 0.999269, 0.999272, 0.999341, 0.999427, 0.99944, 0.999481, 0.999505, 0.999545.
%H A095298 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 A095298 nonn
%Y A095298 A095297, A095334. Cf. also A095353 (similar sums and ratios computed in Fibonacci number system).
%O A095298 1,3
%A A095298 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004


%I A095336
%S A095336 1,3,3,13,20,41,76,176,325,638,1353,2533,5223,10186,20504,40775,80661,
%T A095336 163765,318602,649948,1268922,2571531,5082895,10217300,20327307,40399966,
%U A095336 82164918,160343669,324931245,640501167,1290990369,2567150515,5145601743
%N A095336 Sum of 1-fibits in Zeckendorf-expansion A014417(p) summed for all primes p in range ]2^n,2^(n+1)].
%e A095336 a(1)=1, as only prime in range ]2,4] is 3, whose Fibonacci-representation is 100. In the next range we have primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively, thus  a(2)=3.
%Y A095336 Cf. A095298, A095353.
%H A095336 A. Karttunen, J. Moyer: <a href="http://www.research.att.com/~njas/sequences/primestats.c.txt">C-program for computing the initial terms of this sequence</a>
%K A095336 nonn
%O A095336 1,2
%A A095336 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004


%I A095353
%S A095353 0,0,1,3,2,7,7,14,23,35,56,94,155,243,402,614,1061,1656,2689,4295,
%T A095353 6938,11176,18095,29102,46907,75703,122174,197494,317987,514611,829595,
%U A095353 1340861,2166008,3497040,5645418,9120129,14733126,23803219,38460014
%N A095353 Sum of 1-fibits in Zeckendorf-expansion A014417(p) summed for all primes p in range [Fib(n+1),Fib(n+2)[ (where Fib = A000045).
%e A095353 a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100. a(4)=3, as in [5,8[ there are primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively, and we have three 1-fibits in total. a(5)=2, as in [8,13[ there is only one prime 11, with  Zeckendorf-representation 10100.
%Y A095353 A095336, A095298 (similar sums and ratios computed in binary system).
%H A095353 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>
%C A095353 Ratio a(n)/A095354(n) (i.e. average number of 1-fibits in Zeckendorf-expansions of primes p which Fib(n+1) <= p < Fib(n+2)) grows as: 1, 1, 1, 1.5, 2., 2.333333, 2.333333, 2.8, 3.285714, 3.181818, 3.5, 3.916667, 4.189189, 4.418182, 4.785714, 4.873016, 5.358586, 5.575758, 5.871179, 6.100852, 6.382705, 6.676225, 6.954266, 7.223132, 7.489542, 7.773978, 8.045173, 8.331323, 8.598659, 8.886546, 9.161734, 9.440489, 9.71936, 9.995484, 10.266207, 10.54327, 10.820602, 11.096084, 11.374267.
%C A095353 Ratio of that average compared to A010049(n)/A000045(n) (the expected value of that same sum computed for all integers in the same range) converges as: 1, 1, 0.666667, 0.9, 1, 1.037037, 0.919192, 0.99661, 1.063946, 0.945946, 0.96142, 1, 0.999059, 0.988519, 1.008389, 0.970278, 1.011305, 1.000122, 1.003368, 0.995592, 0.996635, 0.999338, 0.999601, 0.998575, 0.997298, 0.998427, 0.997837, 0.999078, 0.998056, 0.99941, 0.999296, 0.999567, 0.999834, 0.999811, 0.999265, 0.999347, 0.999451, 0.999382, 0.999555.
%K A095353 nonn
%O A095353 1,4
%A A095353 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004

%I A095354
%S A095354 0,0,1,2,1,3,3,5,7,11,16,24,37,55,84,126,198,297,458,704,1087,1674,
%T A095354 2602,4029,6263,9738,15186,23705,36981,57909,90550,142033,222855,
%U A095354 349862,549903,865019,1361581,2145191,3381318,5334509,8419527,13298631
%N A095354 Number of primes p such that Fib(n+1) <= p < Fib(n+2), (where Fib = A000045).
%e A095354 I.e. gives the number of primes whose Zeckendorf-expansion is n fibits long. a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100. a(4)=2, as in [5,8[ there are primes 5 and 7. a(5)=1, as in [8,13[ there is only one prime 11, and a(6)=3 as in [13,21[ there are primes 13,17,19.
%Y A095354 Cf. A095353, A036378.
%H A095354 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 A095354 <a href="http://www.research.att.com/~njas/sequences/Sindx_Pri.html#primepop">Index entries for sequences related to numbers of primes in various ranges</a>
%K A095354 nonn
%O A095354 1,4
%A A095354 Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 04 2004


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Yours,

Antti Karttunen