Number of numbers <= p that are not among the values m! (mod p), where p = prime(n) and m <= 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
It appears that 2 and 3 produce the only zero terms.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Kevin A. Broughan and A. Ross Barnett, On the missing values of n! mod p, J. Ramanujan Math. Soc., 24(3):277–284, 2009.
Oleksiy Klurman and Marc Munsch, Distribution of factorials modulo p, arXiv 1505.01198 (May 05 2015)
(Mma) nn = 100; f = Range[Prime[nn]]!; Table[p - Length[Union[Mod[Take[f, p], p]]], {p, Prime[Range[nn]]}]
Cf. A210184, S000620, S000622.
nonn
T. D. Noe, May 07 2015