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

2,4

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).

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Maple

f:= proc(n) local k, p, q;
    p:= ithprime(n);
    q:= p;
    for k from 0 do
      if isprime(p*q+2) then return k fi;
      q:= nextprime(q);
    od
end proc:
map(f, [$2..100]); # Robert Israel, Apr 15 2026

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 *)

Prog

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

Crossrefs

Cf. A243154.

Sequence in context: A396262 A387975 A385073 * A154723 A273262 A274532

Adjacent sequences: A243155 A243156 A243157 * A243159 A243160 A243161

Keyword

nonn

Author

Vladimir Shevelev, May 31 2014

Extensions

More terms from Colin Barker, May 31 2014

Status

approved