A244916 Primes prime(k) such that 2^(k+1) + prime(k) is also prime.

3, 31, 71, 97, 107, 277, 307, 641, 907, 967, 1009, 1447, 3463, 3527, 7757, 8167, 250867, 279047, 1107791, 1176671, 1538399, 1594909, 2450017

Offset: 1

Author

Robert G. Wilson v, Jul 09 2014

Keywords

• nonn
• more
• hard

Crossrefs

Cf. A078686, A242944, A227126, A228021.

Programs

Maple

for i from 1 do
        p := ithprime(i) ;
        if isprime(p+2^(i+1)) then
                printf("%d,\n",p) ;
        end if;
end do: # R. J. Mathar, Jul 12 2014

Mathematica

p = 2; lst = {}; While[p < 900000, If[ PrimeQ[ 2^(PrimePi@ p +1) + p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst

PARI

lista(nn) = {ip = 1; forprime(p=2, nn, if (isprime(2^(ip+1)+p), print1(p, ", ")); ip++;);} \\ Michel Marcus, Jul 12 2014

Extensions

a(19)-a(23) from Michael S. Branicky, May 31 2025