A245756 Least number k such that (k! + n)/k is prime, or 0 if no such k exists.

1, 1, 3, 1, 0, 1, 0, 2, 3, 1, 0, 1, 0, 0, 3, 1, 0, 1, 0, 2, 0, 1, 0, 2, 5, 0, 3, 1, 0, 1, 0, 2, 3, 0, 5, 1, 0, 38, 0, 1, 0, 1, 0, 2, 3, 1, 0, 0, 7, 0, 3, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 3, 0, 5, 1, 0, 4, 0, 1, 0, 1, 0, 74, 0, 0, 0, 1, 0, 2, 3, 1, 0, 2, 5, 0, 3

Offset: 1

Author

Derek Orr, Jul 31 2014

Keywords

• nonn

Comments

If a(n) = n, then n is in A090660.

a(n) <= n for all n.

a(n) = 1 if and only if n + 1 is prime.

Examples

			(1! + 3)/1 = 4 is not prime.
(2! + 3)/2 = 5/2 is not prime.
(3! + 3)/3 = 3 is prime. Thus a(3) = 3.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A090660.

Programs

PARI

a(n)=for(k=1,n,s=(k!+n)/k;if(floor(s)==s,if(ispseudoprime(s),return(k))))
n=1;while(n<150,print1(a(n),", ");n++)

Extensions

Corrected by Jens Kruse Andersen, Aug 03 2014