A073944 a(n) is the smallest m such that n-th prime divides m! + 1.

1, 2, 4, 3, 5, 12, 16, 9, 14, 18, 30, 36, 40, 21, 23, 52, 15, 8, 18, 7, 72, 23, 13, 88, 96, 100, 6, 106, 86, 112, 63, 65, 16, 16, 50, 150, 156, 81, 166, 172, 89, 180, 95, 102, 196, 99, 210, 222, 61, 228, 64, 210, 240, 97, 31, 131, 9, 93, 40, 280, 282, 45, 63, 220, 312

Offset: 1

Author

Jason Earls, Nov 13 2002

Keywords

• easy
• nonn

Comments

Essentially the same as A072937. - R. J. Mathar, Sep 23 2008

By Wilson's theorem, a(n) < prime(n). Sequence A115092 gives the number of m such that prime(n) divides m!+1. - T. D. Noe, Mar 01 2006, Jan 10 2009

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 2000 terms from T. D. Noe)

Crossrefs

Cf. A038507.

Cf. A072937 (same sequence without a(1)).

Programs

Mathematica

Table[p=Prime[i]; m=1; While[m
0, m++ ]; m, {i,100}] (* T. D. Noe, Mar 01 2006 *)
Module[{sm=Table[{m,m!+1},{m,400}]},Table[SelectFirst[sm,Mod[#[[2]],p]==0&],{p,Prime[ Range[70]]}]][[;;,1]] (* Harvey P. Dale, Sep 15 2023 *)