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 A244919 For odd prime p, largest k such that binomial(2p-1, p-1) 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 (list; graph; refs; listen; history; text; internal format)
 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 R. J. McIntosh, On the converse of Wolstenholme's theorem, Acta Arith., Volume 71, Issue 4 (1995), 381-389. R. J. McIntosh and E. L. Roettger, A search for Fibonacci-Wieferich and Wolstenholme primes, Math. Comp., 76 (2007), 2087-2094. PROG (PARI) forprime(p=3, 10^3, k=1; while(Mod(binomial(2*p-1, p-1), p^k)==1, j=k; k++); if(Mod(binomial(2*p-1, p-1), 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

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Last modified June 18 04:41 EDT 2021. Contains 345098 sequences. (Running on oeis4.)