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

1,1

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A105947 A183846 A219936 * A219582 A177079 A107915

Adjacent sequences: A298943 A298944 A298945 * A298947 A298948 A298949

Keyword

nonn

Author

Felix Fröhlich, Jan 30 2018

Status

approved