A181356 Smallest k such that 2^(2^n) - k is a safe prime.

5, 29, 269, 209, 1469, 15449, 36113, 38117, 1093337, 1942289, 10895177, 43644929, 364486013, 718982153, 2356107437

Offset

2,1

Comments

These numbers are useful as Diffie-Hellman moduli.

Links

Table of n, a(n) for n=2..16.

Mersenne Forum, CRUS-like sieving challenge

Example

a(2)=5 because 2^(2^2) - 5 = 11 is the largest safe prime less than 16.

Prog

(PARI) a(n) = {k = 1; pow2 = 2^(2^n); while (! (isprime(pow2 - k) && isprime((pow2 - k - 1)/2)), k +=2; ); k; } \\ Michel Marcus, Aug 16 2013

Crossrefs

Cf. A058220, A005385, A057821 , A335313.

Sequence in context: A144015 A326986 A228387 * A177440 A292567 A355376

Adjacent sequences: A181353 A181354 A181355 * A181357 A181358 A181359

Keyword

nonn,more,hard

Author

Ken Takusagawa, Jan 27 2011

Extensions

a(14) from Ken Takusagawa, May 31 2011

a(15) from Gary Barnes, Oct 26 2011

a(16) from Mark Andreas, Jan 23 2023

Status

approved