

A244919


For odd prime p, largest k such that binomial(2p1, p1) is congruent to 1 modulo p^k.


3



2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET

2,1


COMMENTS

Wolstenholme's theorem implies that k >= 3 for all p > 3. The prime p is a Wolstenholme prime if and only if k > 3. For the primes up to 10^9 this holds only for p = 16843 and p = 2124679, where in each case a(n) = 4 (i.e. a(1944) = 4 and a(157504) = 4).


LINKS

Table of n, a(n) for n=2..73.
R. J. McIntosh, On the converse of Wolstenholme's theorem, Acta Arith., Volume 71, Issue 4 (1995), 381389.
R. J. McIntosh and E. L. Roettger, A search for FibonacciWieferich and Wolstenholme primes, Math. Comp., 76 (2007), 20872094.


PROG

(PARI) forprime(p=3, 10^3, k=1; while(Mod(binomial(2*p1, p1), p^k)==1, j=k; k++); if(Mod(binomial(2*p1, p1), p^k)!=1, print1(j, ", ")))


CROSSREFS

Cf. A034602, A088164.
Sequence in context: A340944 A270533 A344511 * A158799 A157532 A065684
Adjacent sequences: A244916 A244917 A244918 * A244920 A244921 A244922


KEYWORD

nonn


AUTHOR

Felix FrÃ¶hlich, Jul 08 2014


STATUS

approved



