A095286 Primes in whose binary expansion the number of 1 bits is > 1 + number of 0 bits.

3, 7, 11, 13, 23, 29, 31, 43, 47, 53, 59, 61, 79, 103, 107, 109, 127, 151, 157, 167, 173, 179, 181, 191, 199, 211, 223, 227, 229, 233, 239, 241, 251, 311, 317, 347, 349, 359, 367, 373, 379, 383, 431, 439, 443, 461, 463, 467, 479, 487, 491, 499

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• easy
• base

Examples

			13 is in the sequence because 13 is prime and 13 = 1101_2. '1101' has three 1's and one 0. 3 > 1 + 1. - _Indranil Ghosh_, Feb 07 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..25000
• A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Crossrefs

Complement of A095287 in A000040. Subset of A095070. Subset: A095314. Cf. also A095296.

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 > (b0+1), return(1);, return(0);); };
forprime(x = 3, 499, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 11 2011

Python

from sympy import isprime
i = 1
j = 1
while j <= 2000:
    bi = bin(i)[2:]
    if isprime(i) and bi.count("1") > 1 + bi.count("0"):
        print(str(j) + " " + str(i))
        j += 1
    i += 1 # Indranil Ghosh, Feb 07 2017