A228021 Prime(k) such that 2^(k - 1) + prime(k) is also prime.

2, 3, 29, 89, 251, 659, 937, 1307, 1453, 8179, 9391, 12097, 28499, 83969, 101209, 120739, 730993

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 03 2013

Keywords

• nonn
• hard
• more

Comments

The primes indices k are 1, 2, 10, 24, 54, 120, 159, 214, 231, 1027, 1161, 1447, 3100, 8188, 9695, 11363 ...

The corresponding primes 2^(k - 1) + prime(k) are 3, 5, 541, 8388697,...

a(18) > 2*10^6. - Michael S. Branicky, Apr 16 2025

Examples

			29 is in the sequence because 29 = prime(10) and 2^(10 - 1) + 29 = 512 + 29 = 541 is prime.
		

Crossrefs

Cf. A077375, A227126, A242944, A244913, A244916.

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 < 730001, If[ PrimeQ[ 2^(PrimePi@ p-1) + p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Jul 09 2014 *)

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(3) - a(9) from _Olivier Gérard_, Aug 01 2013

a(10) - a(15) from Robert G. Wilson v, Aug 01 2013

a(16) from Robert G. Wilson v, Jul 09 2014

a(17) from Michael S. Branicky, Apr 14 2025