A095327 -id:A095327 - cp's OEIS frontend

A095317 Primes in whose binary expansion the number of 1 bits is <= number of 0 bits minus 2.

131, 137, 193, 257, 521, 523, 547, 577, 593, 641, 643, 673, 769, 773, 1031, 1033, 1049, 1061, 1091, 1093, 1097, 1153, 1217, 1283, 1289, 1297, 1409, 1553, 1601, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2113, 2129, 2131, 2137, 2153

Offset: 1

Antti Karttunen, Jun 04 2004

Harvey P. Dale, Table of n, a(n) for n = 1..1000
A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095316 in A000040. Subset: A095321. Subset of A095071. Cf. also A095327.

Select[Prime[Range[400]],DigitCount[#,2,1]<=DigitCount[#,2,0]-2&] (* Harvey P. Dale, Dec 10 2017 *)

forprime(p=2,2200,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=-2,print1(p,", ")))
\\ Washington Bomfim, Jan 13 2011

A095326 Number of A095316-primes in range [2^n,2^(n+1)].

Original entry on oeis.org

1, 2, 2, 5, 7, 13, 20, 42, 65, 122, 203, 412, 718, 1413, 2381, 4859, 8266, 16955, 28995, 60484, 105524, 216830, 376969, 785885, 1383287, 2867949, 5044969, 10544609, 18699214, 39034399, 69349061, 145210901, 259051224

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

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

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence
Index entries for sequences related to occurrences of various subsets of primes in range [2^n,2^(n+1)]

a(n) = A036378(n)-A095327(n).

A095294 Number of A095284-primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 4, 4, 8, 15, 44, 47, 150, 236, 701, 863, 2326, 3298, 9354, 12933, 34443, 51300, 134780, 199410, 508200, 769127, 1957824, 2978179, 7424464, 11590386, 28737086, 44867556, 109643089

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

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

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

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence
Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]

a(n) = A036378(n)-A095295(n). Cf. also A095329, A095052, A095053.

cp's OEIS Frontend

A095317 Primes in whose binary expansion the number of 1 bits is <= number of 0 bits minus 2.

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A095326 Number of A095316-primes in range [2^n,2^(n+1)].

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A095294 Number of A095284-primes in range ]2^n,2^(n+1)].

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