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

0,4

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A019434 (Fermat primes).

Sequence in context: A347389 A330774 A296307 * A067292 A131782 A242060

Adjacent sequences: A238551 A238552 A238553 * A238555 A238556 A238557

Keyword

nonn

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Feb 28 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

Status

approved