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

1,2

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.

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 *)

Prog

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

Crossrefs

Cf. A007540, A241014, A244801, A250407.

Sequence in context: A220234 A038020 A211910 * A107094 A122496 A335756

Adjacent sequences: A250403 A250404 A250405 * A250407 A250408 A250409

Keyword

nonn

Author

Felix Fröhlich, Nov 22 2014

Status

approved