A058054 Smallest prime > n! minus largest prime <= n!.

1, 2, 6, 14, 8, 12, 54, 30, 22, 14, 30, 90, 20, 90, 76, 90, 78, 190, 60, 62, 104, 186, 204, 190, 96, 44, 168, 254, 108, 188, 80, 38, 290, 174, 258, 98, 44, 170, 136, 132, 176, 180, 156, 292, 190, 312, 156, 142, 158, 450, 120, 130, 350, 132, 610, 384, 392, 430

Offset: 2

Author

Labos Elemer, Nov 20 2000

Keywords

• nonn

Examples

			For n = 2, 3, 4, 5, A037151(n) = 3, 7, 29, 127 and A006990(n) = 2, 5, 23, 113. The differences are: 1, 2, 6, 14.
		

Links

• Hans Havermann, Table of n, a(n) for n = 2..2000

Crossrefs

Cf. A006990, A037151, A033932, A033933.

Essentially the same as A054588.

Programs

Maple

[seq(nextprime(i!)-prevprime(i!+1), i=2...100)];

Mathematica

f[n_] := NextPrime[n!] - NextPrime[n!, -1]; Array[f, 70, 3] (* Robert G. Wilson v, Jul 23 2014 *)

Formula

a(n) = A037151(n) - A006990(n)

a(n) = A033932(n) + A033933(n)

Extensions

Edited by Hans Havermann, Jul 23 2014