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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

%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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Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)