A095315 Primes in whose binary expansion the number of 1 bits is <= 2 + number of 0 bits.

2, 3, 5, 11, 13, 17, 19, 37, 41, 43, 53, 67, 71, 73, 83, 89, 97, 101, 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, 313, 331, 337, 353, 389, 397

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• easy

Examples

			13 is in the sequence because 13 = 1101_2. '1101' has three 1's and one 0. 3 = 2 + 1. - _Indranil Ghosh_, Feb 07 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..25000 (terms 1..1000 from Harvey P. Dale)
• Antti Karttunen and J. Moyer, C program for computing the initial terms of this sequence

Crossrefs

Complement of A095314 in A000040. Subset: A095287. Subset of A095319. Cf. also A095335.

Programs

Mathematica

Select[Prime[Range[100]],DigitCount[#,2,1]<3+DigitCount[#,2,0]&] (* Harvey P. Dale, Aug 12 2016 *)

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 <= (2+b0), return(1);, return(0););};
forprime(x = 2, 397, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011

Python

from sympy import isprime
i=j=1
while j<=250:
    if isprime(i) and bin(i)[2:].count("1")<=2+bin(i)[2:].count("0"):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 07 2017