A238554 - OEIS

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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

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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