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

Author

Ken Takusagawa, Jan 27 2011

Keywords

• nonn
• more
• hard
• changed

Comments

These numbers are useful as Diffie-Hellman moduli.

Examples

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

Links

• Mersenne Forum, CRUS-like sieving challenge

Crossrefs

Cf. A058220, A005385, A057821, A335313.

Programs

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

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