A245716 Least number k > 0 such that n + k! and n - k! are both prime, or 0 if no such k exists.

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, 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, 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

Offset: 1

Author

Derek Orr, Jul 30 2014

Keywords

• nonn

Comments

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

Examples

			13 + 1! and 13 - 1! are not both prime.
13 + 2! and 13 - 2! are not both prime.
13 + 3! and 13 - 3! are both prime (19 and 7). Thus a(13) = 3.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A245714, A245715.

Programs

PARI

a(n)=for(k=1,n,if(ispseudoprime(n-k!)&&ispseudoprime(n+k!),return(k)))
vector(150,n,a(n))