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A281302 Largest nonnegative k such that binomial(2*c-1, c-1) == 1 (mod c^k), where c is the n-th composite number. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A194670 A130543 A193243 * A160753 A328981 A024360

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

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Last modified November 26 12:37 EST 2020. Contains 338639 sequences. (Running on oeis4.)