Number of nondistinct values among the p-1 terms k! mod p for k = 1..p-1 for primes p.
0, 0, 1, 2, 5, 3, 5, 7, 6, 10, 10, 11, 12, 17, 16, 18, 22, 20, 25, 32, 29, 30, 28, 30, 38, 36, 32, 32, 46, 40, 47, 49, 47, 49, 45, 65, 54, 59, 60, 62, 66, 67, 71, 68, 77, 84, 72, 74, 95, 88, 86, 89, 94, 87, 91, 91, 97, 101, 105, 101, 92, 111, 103, 123, 123, 128
1
Is it possible that this sequence has other 0 terms?
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 = 1000; f = Table[n!, {n, Prime[nn]}]; Table[s = Table[Mod[f[[n]], p], {n, p - 1}]; p - 1 - Length[Union[s]], {p, Prime[Range[nn]]}]
nonn
T. D. Noe, Jan 11 2015