A095285 Primes in whose binary expansion the number of 1 bits is <= 5 + 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, 193, 197, 199, 211, 227, 229, 233, 241, 257, 263, 269, 271, 277, 281, 283

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• base

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. Note that 63 (111111 in binary) is not prime.

Links

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

Crossrefs

Complement of A095284 in A000040. Subset: A095323. Subset of A095313, from which it differs first time at n=42, where a(42)=193 (11000001 in binary) while A095313(42)=191 (10111111 in binary). Cf. also A095286, A095295.

Programs

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 <= (5+b0), return(1);, return(0););};
forprime(x = 2, 283, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011