%I #34 Nov 08 2018 21:13:10
%S 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,
%T 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,
%U 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
%N Largest nonnegative k such that binomial(2*c-1, c-1) == 1 (mod c^k), where c is the n-th composite number.
%C a(n) > 0 if c is either a term of A168363 or a term of A228562.
%C If c is a term of A267824, then a(n) > 1.
%C 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.
%H Antti Karttunen, <a href="/A281302/b281302.txt">Table of n, a(n) for n = 1..25000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Wolstenholme%27s_theorem">Wolstenholme's theorem</a>.
%o (PARI) forcomposite(c=1, , my(k=0); while(Mod(binomial(2*c-1, c-1), c^k)==1, k++); print1(k-1, ", "))
%Y Cf. A002808, A168363, A244919, A267824.
%K nonn
%O 1
%A _Felix Fröhlich_, Jan 21 2017
%E More terms from _Antti Karttunen_, Nov 08 2018
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