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

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

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• base
• easy

Comments

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.

Links

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

Crossrefs

Complement of A095321 in A000040. Subset: A095316.

Cf. A095330.

Programs

Mathematica

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

PARI

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