Number of distinct values among the p-1 terms k! mod p for k = 1..p-1 for primes p.
1, 2, 3, 4, 5, 9, 11, 11, 16, 18, 20, 25, 28, 25, 30, 34, 36, 40, 41, 38, 43, 48, 54, 58, 58, 64, 70, 74, 62, 72, 79, 81, 89, 89, 103, 85, 102, 103, 106, 110, 112, 113, 119, 124, 119, 114, 138, 148, 131, 140, 146, 149, 146, 163, 165, 171, 171, 169, 171, 179
1
The 1000th prime is 7919. So there is much duplication. See S000449.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Tim Trudgian, There are no socialist primes less than 10^9, Integers 14 (2014), A63.
(Mma) nn = 50; f = Table[n!, {n, Prime[nn]}]; Table[s = Table[Mod[f[[n]], p], {n, p - 1}]; Length[Union[s]], {p, Prime[Range[nn]]}];
nonn
T. D. Noe, Jan 11 2015