A260210 A034602(n) modulo prime(n).

1, 5, 1, 1, 3, 9, 13, 11, 1, 11, 34, 33, 31, 38, 58, 56, 24, 35, 62, 38, 23, 27, 96, 84, 2, 66, 106, 74, 10, 31, 8, 34, 58, 26, 26, 144, 150, 140, 167, 137, 31, 107, 78, 157, 1, 103, 165, 97, 111, 60, 196, 48, 97, 259, 155, 175, 244, 13, 269, 34, 184, 222, 54

Offset: 3

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 with a(n) <= c in order to get a larger data set.

The values here appear to have a nicer asymptotic growth behavior than those in A260209.

It appears that A260209(n)/a(n) = A001248(n).

The formula only returns integers for primes greater than 3. - Robert G. Wilson v, Jul 29 2015

Links

• Felix Fröhlich, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A034602, A088164, A241014, A244801, A250406, A258367, A260209.

Programs

Mathematica

f[n_] := Block[{p = Prime@ n}, (Mod[ Binomial[2p - 1, p - 1], p^4] - 1)/p^3]; Array[f, 60, 3] (* Robert G. Wilson v, Jul 29 2015 *)

PARI

a(n) = p=prime(n); lift(Mod(binomial(2*p-1, p-1)\p^3, p))

Formula

A034602(n)/prime(n) = A260209(n)/prime(n)^2, for n>2. - Robert G. Wilson v, Jul 29 2015