A243158 - OEIS

%I #19 Apr 16 2026 00:52:01

%S 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,

%T 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,

%U 7,2,26,19,6,2,8,30,23,6,19,5,1,1,12,1,7

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

%C 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).

%H Robert Israel, <a href="/A243158/b243158.txt">Table of n, a(n) for n = 2..10000</a>

%p f:= proc(n) local k,p,q;

%p     p:= ithprime(n);

%p     q:= p;

%p     for k from 0 do

%p       if isprime(p*q+2) then return k fi;

%p       q:= nextprime(q);

%p     od

%p end proc:

%p map(f, [$2..100]); # _Robert Israel_, Apr 15 2026

%t 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 *)

%o (PARI) vector(200, n, k=0; while(!isprime(prime(n+1)*prime(n+1+k)+2), k++); k) \\ _Colin Barker_, May 31 2014

%Y Cf. A243154.

%K nonn

%O 2,4

%A _Vladimir Shevelev_, May 31 2014

%E More terms from _Colin Barker_, May 31 2014