A057662 Smallest prime q such that q + 2^prime(n) is a prime, where prime(n) is the n-th prime.

3, 3, 5, 3, 5, 17, 29, 53, 11, 11, 11, 29, 71, 29, 5, 5, 131, 197, 3, 11, 29, 23, 89, 29, 359, 149, 239, 239, 881, 281, 29, 3449, 197, 683, 389, 683, 101, 1283, 83, 191, 1181, 197, 5, 71, 107, 101, 71, 4001, 1433, 251, 431, 29, 1361, 89, 509, 83, 2459, 941, 101, 197

Offset: 1

Author

Labos Elemer, Oct 16 2000

Keywords

• nonn

Examples

			For n = 6, prime(6) = 13, 8192 + 17 = 8209 is a prime but 8192 + 2, 8182 + 3, ..., 8192 + 13 are not, so a(6) = 17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A056206, A056208.

Programs

Mathematica

a[n_] := Module[{m = 2^Prime[n], q = 2}, While[!PrimeQ[q + m], q = NextPrime[q]]; q]; Array[a, 60] (* Amiram Eldar, Mar 13 2025 *)

PARI

a(n) = my(P=2^prime(n), q=2); while (!isprime(P+q), q = nextprime(q+1)); q; \\ Michel Marcus, Mar 04 2022

Formula

a(n) = A056206(A000040(n)).