A250406 Values of B such that p = prime(n) satisfies (p-1)! == -1-B*p (mod p^2), i.e., p is a near-Wilson prime.

1, 2, 0, 2, 10, 0, 12, 17, 15, 11, 12, 30, 25, 30, 41, 19, 32, 5, 55, 2, 62, 6, 63, 19, 27, 29, 46, 106, 79, 18, 56, 12, 81, 72, 55, 65, 6, 55, 146, 67, 131, 109, 32, 158, 50, 81, 38, 43, 114, 98, 64, 132, 45, 37, 80, 190, 148, 101, 252, 4, 119, 62, 36, 52, 25

Offset: 1

Author

Felix Fröhlich, Nov 22 2014

Keywords

• nonn

Comments

p is in A007540 iff a(n) == 0.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000
• E. Costa, R. Gerbicz and D. Harvey, A search for Wilson primes, Math. Comp., 83 (2014), 3071-3091.
• R. Crandall, K. Dilcher and C. Pomerance, A search for Wieferich and Wilson primes, Math. Comp., 66 (1997), 433-449.

Crossrefs

Cf. A007540, A241014, A244801, A250407.

Programs

Mathematica

f[n_] := Block[{k = 0, m, p = Prime[n]}, m = Mod[(p - 1)!, p^2]; While[ Mod[-1 - k*p, p^2] != m, k++]; k]; Array[f, 70] (* Robert G. Wilson v, Dec 03 2014 *)

PARI

forprime(p=1, 1e9, b=0; while(Mod((p-1)!, p^2)!=-1-b*p, b++); print1(b, ", "))