A260209 Values A such that p=prime(n) satisfies binomial(2p-1, p-1) == 1 + A*p (mod p^4).

1, 3, 25, 245, 121, 169, 867, 3249, 6877, 9251, 961, 15059, 57154, 61017, 68479, 106742, 201898, 208376, 107736, 176435, 330398, 237158, 158447, 213867, 903264, 856884, 21218, 755634, 1259386, 944906, 161290, 531991, 150152, 656914, 1287658, 592826, 640874

Offset: 1

Author

Felix Fröhlich, Jul 19 2015

Keywords

• nonn

Comments

p is a Wolstenholme prime (A088164) iff a(n) == 0. This holds for n = 1944 and n = 157504.

When performing a search for Wolstenholme primes, one can choose an integer constant c >= 0 and record all primes p with A <= c in order to get a larger data set.

The values here asymptotically appear to grow more quickly than those in A260210.

It appears that a(n)/A260210(n) = A001248(n) for all n.

Links

• Felix Fröhlich, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088164, A241014, A244801, A250406, A258367, A260210.

Programs

Mathematica

f[n_] := Block[{p = Prime@ n}, (Mod[ Binomial[2p - 1, p - 1], p^4] - 1)/p]; Array[f, 37] (* Robert G. Wilson v, Jul 29 2015 *)

PARI

a(n) = p=prime(n); (lift(Mod(binomial(2*p-1, p-1), p^4))-1)/p