A095321 -id:A095321 - cp's OEIS frontend

A095331 Number of A095321-primes in range ]2^n,2^(n+1)].

0, 0, 0, 0, 0, 0, 0, 1, 4, 15, 14, 52, 83, 199, 260, 850, 1204, 3435, 4596, 13102, 19095, 51386, 72485, 199933, 296317, 777795, 1152625, 3017298, 4571188, 11663138, 17768490, 45124684, 70038513

Offset: 1

Antti Karttunen, Jun 04 2004

nonn

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

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)-A095330(n).

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

Original entry on oeis.org

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

A095320 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 3.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 263, 269

Offset: 1

Antti Karttunen, Jun 04 2004

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.

A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Complement of A095321 in A000040. Subset: A095316.

Cf. A095330.

Select[Prime[Range[60]],DigitCount[#,2,1]>DigitCount[#,2,0]-3&] (* Harvey P. Dale, Jul 24 2013 *)

forprime(p=2,269,v=binary(p);s=0;for(k=1,#v,    s+=if(v[k]==1,+1,-1));if(s>-3,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011

cp's OEIS Frontend

A095331 Number of A095321-primes in range ]2^n,2^(n+1)].

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

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PARI

A095320 Primes in whose binary expansion the number of 1-bits is > number of 0-bits minus 3.

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Mathematica

PARI