A038204 Least k such that factorials have exactly n distinct residues mod k.

1, 2, 3, 5, 7, 11, 22, 25, 55, 13, 26, 17, 34, 57, 76, 95, 23, 46, 29, 58, 31, 62, 93, 155, 319, 37, 74, 129, 41, 82, 47, 94, 141, 235, 53, 106, 59, 118, 71, 142, 61, 67, 134, 73, 146, 219, 365, 511, 79, 158, 237, 395, 553, 1241, 83, 166, 332, 747, 89, 178, 291, 485

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A038203.

Programs

Mathematica

s = Table[Length@ Union@ Mod[Range[10^3]!, n], {n, 2000}]; Table[FirstPosition[s, n], {n, 62}] // Flatten (* Michael De Vlieger, Aug 03 2016, Version 10 *)

PARI

a(n)=my(k=n,t=1); while(#Set(vector(k,i,t=(t*i)%k))!=n, k++; t=1); k \\ Charles R Greathouse IV, Aug 03 2016