Irregular table of k! mod p for k = 1..p-1 for primes p.
1, 1, 2, 1, 2, 1, 4, 1, 2, 6, 3, 1, 6, 1, 2, 6, 2, 10, 5, 2, 5, 1, 10, 1, 2, 6, 11, 3, 5, 9, 7, 11, 6, 1, 12, 1, 2, 6, 7, 1, 6, 8, 13, 15, 14, 1, 12, 3, 8, 1, 16, 1, 2, 6, 5, 6, 17, 5, 2, 18, 9, 4, 10, 16, 15, 16, 9, 1, 18, 1, 2, 6, 1, 5, 7, 3, 1, 9, 21, 1, 12, 18, 22, 8, 13, 14, 22, 4, 11, 1, 22
1
The p-1 numbers k! mod p are distinct for p = 2 and 3. It is unknown whether it is true for additional primes. Sequences S000448 and S000449 explore this.
T. D. Noe, Plot of 50 rows
T. D. Noe, Table of 50 rows
Tim Trudgian, There are no socialist primes less than 10^9, Integers 14 (2014), A63.
(Mma) Table[Table[Mod[n!, p], {n, p - 1}], {p, Prime[Range[10]]}]
nonn,tabf,nice
T. D. Noe, Jan 11 2015