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%I #13 Mar 05 2022 14:17:24
%S 2,3,5,7,11,13,19,31,23,19,17,43,73,41,149,41,53,61,109,37,37,71,109,
%T 193,97,173,47,101,229,163,241,83,139,103,83,577,311,47,269,61,61,107,
%U 97,89,379,149,269,83,137,167,281,89,79,443,229,157,179,563,389
%N a(n) = p - n!, where p is the second smallest prime > n!.
%C p-n! where p = nextprime(nextprime(n!)).
%C Is every term a prime?
%H Clark Kimberling, <a href="/A275272/b275272.txt">Table of n, a(n) for n = 1..300</a>
%F a(n) = A187874(n) - A000142(n). - _Michel Marcus_, Mar 05 2022
%e For n = 4, we have n! = 24, so that p = 31 and a(4) = 7.
%t Table[NextPrime[n!, 2] - n!, {n, 1, 150}]
%o (PARI) a(n) = nextprime(nextprime(n!+1)+1) - n!; \\ _Michel Marcus_, Mar 05 2022
%o (Python)
%o from sympy import factorial, nextprime
%o def a(n): fn = factorial(n); return nextprime(nextprime(fn)) - fn
%o print([a(n) for n in range(1, 60)]) # _Michael S. Branicky_, Mar 05 2022
%Y Cf. A037153, A005235, A275273, A275274, A000040.
%Y Cf. A000142, A187874.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jul 23 2016