A095313 Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.

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, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• base
• easy

Comments

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.

Links

• 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

Crossrefs

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.

Programs

Mathematica

Select[Prime[Range[100]],DigitCount[#,2,1]<= DigitCount[#,2,0]+6&] (* Harvey P. Dale, Aug 18 2016 *)

PARI

forprime(p=2,269,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=6,print1(p,", "))) \\ Washington Bomfim, Jan 13 2011