A095075 Primes in whose binary expansion the number of 1-bits is less than or equal to number of 0-bits.

2, 17, 37, 41, 67, 73, 97, 131, 137, 139, 149, 163, 193, 197, 257, 263, 269, 277, 281, 293, 337, 353, 389, 401, 449, 521, 523, 541, 547, 557, 563, 569, 577, 587, 593, 601, 613, 617, 641, 643, 647, 653, 659, 661, 673, 677, 709, 769, 773, 787

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• easy
• base

Examples

			From _Indranil Ghosh_, Feb 03 2017: (Start)
17 is in the sequence because 17_10 = 10001_2. '10001' has two 1's and three 0's.
37 is in the sequence because 37_10 = 100101_2. '100101' has three 1's and 3 0's. (End)
		

Links

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

Crossrefs

Complement of A095070 in A000040.

Cf. A095055.

Programs

Mathematica

Select[Prime[Range[150]], Differences[DigitCount[#, 2]][[1]] >= 0 &] (* Amiram Eldar, Jul 25 2023 *)
Select[Prime[Range[150]],DigitCount[#,2,1]<=DigitCount[#,2,0]&] (* Harvey P. Dale, Sep 27 2023 *)

PARI

B(x) = {nB = floor(log(x)/log(2)); z1 = 0; z0 = 0;
for(i = 0, nB, if(bittest(x,i), z1++;, z0++;); );
if(z1 <= z0, return(1);, return(0););};
forprime(x = 2, 787, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 11 2011

Python

from sympy import isprime
i=1
j=1
while j<=250:
    if isprime(i) and bin(i)[2:].count("1")<=bin(i)[2:].count("0"):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 03 2017