A238554 Smallest k such that k + 2^n and k*2^n + 1 are both prime.

1, 1, 1, 5, 1, 11, 3, 9, 1, 35, 15, 39, 3, 39, 63, 35, 1, 149, 3, 419, 7, 221, 25, 155, 73, 735, 69, 29, 193, 261, 3, 135, 81, 149, 85, 125, 117, 809, 303, 509, 27, 699, 325, 29, 27, 285, 639, 65, 61, 1911, 639, 165, 295, 1295, 163, 905, 175, 75, 1593, 249

Offset: 0

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Feb 28 2014

Keywords

• nonn

Comments

If a(n) = 1, then the two primes are the same and they are Fermat primes. - Michel Marcus, Mar 01 2014

Examples

			5 is in this sequence because 5 + 2^3 = 13 and 5*2^3 + 1 = 41 are both prime.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A019434 (Fermat primes).

Programs

Mathematica

Table[Module[{k=1,c=2^n},While[!AllTrue[{c+k,k c+1},PrimeQ],k++];k],{n,0,60}] (* Harvey P. Dale, Oct 20 2023 *)

PARI

a(n) = {k = 1;while (!(isprime(k + 2^n) && isprime(k*2^n + 1)), k++); k;} \\ Michel Marcus, Mar 01 2014

Extensions

a(15) corrected and a(24) from Michel Marcus, Mar 01 2014

Missing term and a(25)-a(59) from Giovanni Resta, Mar 01 2014