A245716 - OEIS

%I #11 Jul 30 2014 20:25:58

%S 0,0,0,1,2,1,0,0,2,0,3,1,3,0,2,0,3,1,0,0,2,0,3,0,3,0,0,0,4,1,0,0,0,0,

%T 3,0,3,0,2,0,0,1,4,0,2,0,3,0,0,0,0,0,3,0,4,0,0,0,0,1,0,0,0,0,3,0,3,0,

%U 2,0,0,1,3,0,0,0,3,0,0,0,2,0,4,0,4,0,0,0,0,0,0,0,0,0,3,0,0,0,2,0,0,1,3,0,2,0,3,1,0,0,2,0,4,0,0,0,0,0,0,0

%N Least number k > 0 such that n + k! and n - k! are both prime, or 0 if no such k exists.

%C For a(n) > 0, a(n)! < n for all n. Thus a(n) = 0 is definite.

%H Jens Kruse Andersen, <a href="/A245716/b245716.txt">Table of n, a(n) for n = 1..10000</a>

%e 13 + 1! and 13 - 1! are not both prime.

%e 13 + 2! and 13 - 2! are not both prime.

%e 13 + 3! and 13 - 3! are both prime (19 and 7). Thus a(13) = 3.

%o (PARI)

%o a(n)=for(k=1,n,if(ispseudoprime(n-k!)&&ispseudoprime(n+k!),return(k)))

%o vector(150,n,a(n))

%Y Cf. A245714, A245715.

%K nonn

%O 1,5

%A _Derek Orr_, Jul 30 2014