A243158 Smallest k>=0 such that prime(n)*prime(n+k) + 2 is prime.

0, 1, 1, 3, 1, 5, 1, 3, 4, 4, 3, 5, 2, 6, 13, 5, 6, 1, 9, 28, 8, 2, 10, 8, 5, 8, 3, 3, 31, 2, 2, 9, 6, 1, 3, 6, 2, 5, 4, 1, 10, 3, 7, 3, 6, 7, 4, 4, 1, 14, 1, 1, 4, 4, 18, 1, 8, 1, 3, 10, 3, 1, 6, 1, 7, 2, 26, 19, 6, 2, 8, 30, 23, 6, 19, 5, 1, 1, 12, 1, 7

Offset: 2

Author

Vladimir Shevelev, May 31 2014

Keywords

• nonn

Comments

A dual sequence to A243154. The sequence contains a unique zero term. Indeed, every prime p>3 has the form 3*k +/- 1. So, p^2 + 2 == 0 (mod 3).

Crossrefs

Cf. A243154.

Programs

Mathematica

skp[n_]:=Module[{c=Prime[n],k=0},While[!PrimeQ[c*Prime[n+k]+2],k++];k]; Array[ skp,90,2] (* Harvey P. Dale, May 08 2021 *)

PARI

vector(200, n, k=0; while(!isprime(prime(n+1)*prime(n+1+k)+2), k++); k) \\ Colin Barker, May 31 2014

Extensions

More terms from Colin Barker, May 31 2014