A275272 a(n) = p - n!, where p is the second smallest prime > n!.

2, 3, 5, 7, 11, 13, 19, 31, 23, 19, 17, 43, 73, 41, 149, 41, 53, 61, 109, 37, 37, 71, 109, 193, 97, 173, 47, 101, 229, 163, 241, 83, 139, 103, 83, 577, 311, 47, 269, 61, 61, 107, 97, 89, 379, 149, 269, 83, 137, 167, 281, 89, 79, 443, 229, 157, 179, 563, 389

Offset: 1

Author

Clark Kimberling, Jul 23 2016

Keywords

• nonn
• easy

Comments

p-n! where p = nextprime(nextprime(n!)).

Is every term a prime?

Examples

			For n = 4, we have n! = 24, so that p = 31 and a(4) = 7.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A037153, A005235, A275273, A275274, A000040.

Cf. A000142, A187874.

Programs

Mathematica

Table[NextPrime[n!, 2] - n!, {n, 1, 150}]

PARI

a(n) = nextprime(nextprime(n!+1)+1) - n!; \\ Michel Marcus, Mar 05 2022

Python

from sympy import factorial, nextprime
def a(n): fn = factorial(n); return nextprime(nextprime(fn)) - fn
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Mar 05 2022

Formula

a(n) = A187874(n) - A000142(n). - Michel Marcus, Mar 05 2022