A074928 a(n) is the least k>0 such that prime(n)*prime(n+1) + k is prime.

1, 2, 2, 2, 6, 2, 8, 2, 6, 8, 4, 6, 14, 6, 12, 10, 8, 4, 2, 6, 12, 6, 6, 8, 6, 24, 6, 14, 6, 18, 12, 10, 8, 6, 2, 12, 10, 18, 10, 4, 2, 12, 8, 18, 6, 10, 4, 6, 8, 2, 4, 2, 2, 6, 10, 6, 2, 12, 2, 8, 20, 8, 2, 24, 2, 6, 30, 14, 20, 6, 6, 6, 6, 4, 20, 4, 6, 2, 2, 12, 2, 6, 6, 6, 2, 22, 8, 32, 6, 12

Offset

1,2

Comments

a(n) is even for n > 1. - Seiichi Manyama, Mar 17 2025

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 because prime(1)*prime(2) + 1 = 2*3 + 1 = 7 -> prime.

Mathematica

NextPrime[#]-#&/@Times@@@Partition[Prime[Range[100]], 2, 1] (* Harvey P. Dale, May 28 2013 *)

Prog

(PARI) a(n) = my(k=1, q=prime(n)*prime(n+1)); while (!isprime(q+k), k++); k; \\ Michel Marcus, Jun 05 2026

Crossrefs

Cf. A107019, A107057, A107058.

Sequence in context: A023957 A224964 A278165 * A285713 A278230 A344859

Adjacent sequences: A074925 A074926 A074927 * A074929 A074930 A074931

Keyword

nonn,changed

Author

Zak Seidov, Oct 02 2002

Extensions

Name edited by Michel Marcus, Jun 05 2026

Status

approved