A095319 Primes in whose binary expansion the number of 1 bits is <= 3 + number of 0 bits.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 53, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 211, 227, 229, 233, 241, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

Author

Antti Karttunen

Keywords

• nonn
• base
• easy

Comments

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

Links

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

Crossrefs

Complement of A095318 in A000040. Subset of A095323, subset: A095315. A095329.

Programs

Mathematica

Select[Prime[Range[70]],DigitCount[#,2,1]Harvey P. Dale, Feb 22 2020 *)

PARI

B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 <= (3+b0), return(1);, return(0););};
forprime(x = 2, 311, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011