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

2,2

Comments

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A075694 A186300 A323650 * A144751 A138847 A235699

Adjacent sequences: A350693 A350694 A350695 * A350697 A350698 A350699

Keyword

nonn

Author

Mark Andreas, Jan 12 2022

Status

approved