A095314 Primes in whose binary expansion the number of 1 bits is > 2 + number of 0 bits.

7, 23, 29, 31, 47, 59, 61, 79, 103, 107, 109, 127, 191, 223, 239, 251, 311, 317, 347, 349, 359, 367, 373, 379, 383, 431, 439, 443, 461, 463, 467, 479, 487, 491, 499, 503, 509, 607, 631, 701, 719, 727, 733, 743, 751, 757, 761, 823, 827, 829, 859

Offset: 1

Author

Antti Karttunen, Jun 04 2004

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• A. Karttunen and J. Moyer: C-program for computing the initial terms of this sequence

Crossrefs

Complement of A095315 in A000040. Subset of A095286. Subset: A095318. Cf. also A095334.

Programs

Maple

f:= proc(n) local L,d,s;
    if not isprime(n) then return false fi;
    L:= convert(n,base,2);
    convert(L,`+`) > nops(L)/2+1
end proc:
select(f, [seq(i,i=3..1000,2)]); # Robert Israel, Oct 26 2023

Mathematica

n1Q[p_]:=Module[{be=IntegerDigits[p,2]},Total[be]>2+Count[be,0]]; Select[ Prime[ Range[150]],n1Q] (* Harvey P. Dale, Oct 26 2022 *)

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, 859, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011