A066148 Primes with an even number of 0's in binary expansion.

3, 7, 19, 31, 43, 53, 67, 73, 79, 97, 103, 107, 109, 127, 139, 149, 163, 197, 271, 283, 307, 313, 331, 367, 379, 397, 409, 419, 421, 431, 433, 439, 443, 457, 463, 487, 491, 499, 523, 547, 571, 593, 599, 619, 643, 673, 683, 691, 739, 751, 773, 797, 811, 821

Offset: 1

Author

R. K. Guy, Dec 13 2001

Keywords

• nonn
• easy
• base

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A066149, A027699, A027697.

Cf. A059010

Programs

Mathematica

Select[Prime[Range[200]],EvenQ[DigitCount[#,2,0]]&] (* Harvey P. Dale, Mar 04 2017 *)

PARI

a066148(m) = local(p,v,z); forprime(p=2,m,v=binary(p); z=0; for(j=1,matsize(v)[2], if(v[j]==0,z++)); if(z%2==0,print1(p,",")))
a066148(850)

PARI

f(p)={v=binary(p);s=0;for(k=1,#v,if(v[k]==0, s++));return(1-s%2)};forprime(p=3,821,if(f(p),print1(p,", "))) \\ Washington Bomfim, Jan 14 2011

PARI

forprime(p=2, 10^3, if( #select(x->x==0, digits(p,2))%2==0, print1(p,", "))); \\ Joerg Arndt, Jun 16 2018

Extensions

More terms from Vladeta Jovovic and Klaus Brockhaus, Dec 13 2001