A260209 - OEIS

%I #24 Aug 18 2015 12:24:22

%S 1,3,25,245,121,169,867,3249,6877,9251,961,15059,57154,61017,68479,

%T 106742,201898,208376,107736,176435,330398,237158,158447,213867,

%U 903264,856884,21218,755634,1259386,944906,161290,531991,150152,656914,1287658,592826,640874

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

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

%C 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.

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

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

%H Felix Fröhlich, <a href="/A260209/b260209.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 *)

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

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

%K nonn

%O 1,2

%A _Felix Fröhlich_, Jul 19 2015