A281302 Largest nonnegative k such that binomial(2*c-1, c-1) == 1 (mod c^k), where c is the n-th composite number.

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1

Comments

a(n) > 0 if c is either a term of A168363 or a term of A228562.

If c is a term of A267824, then a(n) > 1.

If there is a composite c that is a counterexample to the converse of Wolstenholme's theorem, that composite has a(i) > 2, where i is the index of c in A002808.

Links

Antti Karttunen, Table of n, a(n) for n = 1..25000

Wikipedia, Wolstenholme's theorem.

Prog

(PARI) forcomposite(c=1, , my(k=0); while(Mod(binomial(2*c-1, c-1), c^k)==1, k++); print1(k-1, ", "))

Crossrefs

Cf. A002808, A168363, A244919, A267824.

Sequence in context: A185013 A346459 A193243 * A369426 A340599 A160753

Adjacent sequences: A281299 A281300 A281301 * A281303 A281304 A281305

Keyword

nonn

Author

Felix Fröhlich, Jan 21 2017

Extensions

More terms from Antti Karttunen, Nov 08 2018

Status

approved