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A242473 Binomial(2p-1,p-1) modulo p^4, with p=prime(n).

%I A242473 #68 Apr 25 2025 05:42:02
%S A242473 3,10,126,1716,1332,2198,14740,61732,158172,268280,29792,557184,
%T A242473 2343315,2623732,3218514,5657327,11911983,12710937,7218313,12526886,
%U A242473 24119055,18735483,13151102,19034164,87616609,86545285,2185455,80852839,137273075,106774379,20483831,69690822,20570825
%N A242473 Binomial(2p-1,p-1) modulo p^4, with p=prime(n).
%C A242473 A value of 1 indicates a Wolstenholme prime.
%H A242473 Chai Wah Wu, <a href="/A242473/b242473.txt">Table of n, a(n) for n = 1..10000</a>
%t A242473 Table[Mod[Binomial[2p-1,p-1],p^4],{p,Prime[Range[30]]}] (* _Harvey P. Dale_, Jun 26 2017 *)
%o A242473 (PARI) forprime(n=2, 10^2, m=(binomial(2*n-1, n-1)%n^4); print1(m, ", "));
%o A242473 (Python)
%o A242473 from __future__ import division
%o A242473 from sympy import isprime
%o A242473 A242473_list, b = [], 1
%o A242473 for n in range(1,10**4):
%o A242473     if isprime(n):
%o A242473         A242473_list.append(b % n**4)
%o A242473     b = b*2*(2*n+1)//(n+1) # _Chai Wah Wu_, Jan 26 2016
%o A242473 (Python)
%o A242473 from sympy import Mod, binomial, prime
%o A242473 def A242473(n): return int(Mod(binomial(2*(p:=prime(n))-1,p-1,evaluate=False),p**4)) # _Chai Wah Wu_, Apr 24 2025
%Y A242473 Cf. A088164, A099905, A099906, A099907. Subsequence of A099908.
%K A242473 nonn
%O A242473 1,1
%A A242473 _Felix Fröhlich_, May 26 2014