A095079 Primes with two 0-bits in their binary expansion.

19, 43, 53, 79, 103, 107, 109, 367, 379, 431, 439, 443, 463, 487, 491, 499, 751, 863, 887, 983, 1013, 1279, 1471, 1531, 1663, 1759, 1783, 1787, 1789, 1951, 1979, 1999, 2011, 2027, 2029, 3067, 3581, 3823, 4027, 5119, 6079, 6911, 7039, 7103

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• base
• easy

Links

• Alois P. Heinz, 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

Cf. A095059.

Programs

Mathematica

Select[Prime[Range[1000]], DigitCount[#, 2, 0] == 2 &]

PARI

{ forprime(p=2,8000,
  v=binary(p); s=0;
  for(k=1,#v, s+=if(v[k]==0,+1,0));
  if(s==2,print1(p,", "))
) }

Python

from sympy import isprime
from itertools import combinations, count, islice
def agen(): # generator of terms
    for d in count(2):
        b = (1<<(d+2))-1
        for i, j in combinations(range(d), 2):
            if isprime(t:=b-(1<<(d-i))-(1<<(d-j))):
                yield t
print(list(islice(agen(), 43))) # Michael S. Branicky, Dec 27 2023