A298946 a(n) = binomial(2*c-1, c-1) (mod c^4), where c is the n-th composite number.

35, 462, 2339, 4627, 2378, 4238, 5148, 1260, 57635, 85026, 64410, 100509, 163716, 171918, 93876, 309780, 148969, 444220, 370712, 532771, 652200, 938386, 816466, 907874, 569300, 1107298, 2470810, 2953692, 887812, 1341810, 2956584, 1941390, 589961, 6248628

Offset: 1

Author

Felix Fröhlich, Jan 30 2018

Keywords

• nonn

Comments

Composites c where a(n) = 1 could be called "Wolstenholme pseudoprimes". Do any such composites exist?

A necessary condition for c to be a "Wolstenholme pseudoprime" would be that it is a term of A228562 or A267824.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088164, A228562, A244214, A267824, A281302, A298944, A298945.

Programs

Maple

R:= NULL:
count:= 0: F:= 10;
for n from 4 while count < 100 do
  F:= F * (4*n-2)/n;
  if not isprime(n) then
     count:= count+1;
     R:= R, F mod (n^4);
  fi
od:
R; # Robert Israel, Feb 02 2018

Mathematica

Table[Mod[Binomial[2 c - 1, c - 1], c^4], {c, Select[Range@ 50, CompositeQ]}] (* Michael De Vlieger, Feb 01 2018 *)

PARI

forcomposite(c=1, 200, print1(lift(Mod(binomial(2*c-1, c-1), c^4)), ", "))

Python

from sympy import binomial, composite
def A298946(n):
    c = composite(n)
    return binomial(2*c-1,c-1) % c**4 # Chai Wah Wu, Feb 02 2018