A350696 a(n) is the least nonnegative integer k such that 2^n + k is a safe prime.

1, 3, 7, 15, 19, 39, 7, 51, 163, 15, 31, 231, 103, 75, 7, 195, 499, 99, 127, 627, 955, 555, 691, 87, 679, 99, 1411, 351, 799, 135, 91, 771, 79, 951, 667, 975, 1183, 1311, 667, 315, 955, 759, 2011, 9315, 4243, 1575, 907, 1527, 3943, 2091, 1927, 75, 1879

Offset: 2

Author

Mark Andreas, Jan 12 2022

Keywords

• nonn

Comments

2^n+a(n) is the smallest (n+1)-bit safe prime.

Examples

			a(6)=19 because 2^6+19=83 is the smallest safe prime greater than 64 of the form p=2q+1 where p and q are both primes.
		

Links

• Mark Andreas, Table of n, a(n) for n = 2..5120

Crossrefs

Cf. A111671, A057821, A243916, A181356, A335313.

Programs

Mathematica

safeQ[p_] := And @@ PrimeQ[{p, (p - 1)/2}]; a[n_] := Module[{k = 2^n + 1}, While[! safeQ[k], k++]; k -= 2^n]; Array[a, 50, 2] (* Amiram Eldar, Jan 12 2022 *)

PARI

a(n) = {my(k=0); until (isprime(2^n+k) && isprime((2^n+k-1)/2), k++); return (k); }