Number of composite numbers around n!.
0, 0, 1, 5, 13, 7, 11, 53, 29, 21, 13, 29, 89, 19, 89, 75, 89, 77, 189, 59, 61, 103, 185, 203, 189, 95, 43, 167, 253, 107, 187, 79, 37, 289, 173, 257, 97, 43, 169, 135, 131, 175, 179, 155, 291, 189, 311, 155, 141, 157, 449, 119, 129, 349, 131, 609, 383, 391
1
Note that a(n) > n for n > 3.
T. D. Noe, Plot of 500 terms
T. D. Noe, Table of 500 terms
(Mma) Join[{0, 0}, Table[NextPrime[n!] - NextPrime[n!, -1] - 1, {n, 3, 50}]]
nonn
T. D. Noe, Mar 20 2015