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A298946 a(n) = binomial(2*c-1, c-1) (mod c^4), where c is the n-th composite number. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 00:02 EDT 2022. Contains 353931 sequences. (Running on oeis4.)