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

3, 10, 126, 1716, 1332, 2198, 14740, 61732, 158172, 268280, 29792, 557184, 2343315, 2623732, 3218514, 5657327, 11911983, 12710937, 7218313, 12526886, 24119055, 18735483, 13151102, 19034164, 87616609, 86545285, 2185455, 80852839, 137273075, 106774379, 20483831, 69690822, 20570825

Offset: 1

Author

Felix Fröhlich, May 26 2014

Keywords

• nonn

Comments

A value of 1 indicates a Wolstenholme prime.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088164, A099905, A099906, A099907. Subsequence of A099908.

Programs

Mathematica

Table[Mod[Binomial[2p-1,p-1],p^4],{p,Prime[Range[30]]}] (* Harvey P. Dale, Jun 26 2017 *)

PARI

forprime(n=2, 10^2, m=(binomial(2*n-1, n-1)%n^4); print1(m, ", "));

Python

from _future_ import division
from sympy import isprime
A242473_list, b = [], 1
for n in range(1,10**4):
    if isprime(n):
        A242473_list.append(b % n**4)
    b = b*2*(2*n+1)//(n+1) # Chai Wah Wu, Jan 26 2016

Python

from sympy import Mod, binomial, prime
def A242473(n): return int(Mod(binomial(2*(p:=prime(n))-1,p-1,evaluate=False),p**4)) # Chai Wah Wu, Apr 24 2025