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A282410
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a(n) = binomial(2*p-1, p-1) modulo p^5, where p = prime(n).
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1
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3, 10, 126, 1716, 30614, 2198, 1100513, 713337, 4635628, 4511966, 15729649, 49285370, 10820598, 115444165, 110571496, 84562137, 145202954, 386548644, 208729523, 1232287574, 790871562, 2277840181, 3525066856, 4912928962, 7258488370, 8723558568, 9006255935
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) != 1 for all n (cf. McIntosh, 1995, p. 387).
See arXiv:1502.05750, Theorem 2 for several conditions equivalent to p having a(n) = 1.
Clearly, a prime p such that a(n) = 1 must be a Wolstenholme prime, i.e., a term of A088164.
a(n) is prime for n: 1, 7, 19, 59, 76, 92, 109, 112, 165, 196, 221, 249, 263, 326, etc. Robert G. Wilson v, Feb 14 2017
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LINKS
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MATHEMATICA
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f[n_] := Block[{p = Prime@n}, Mod[ Binomial[ 2p -1, p -1], p^5]]; Array[f, 27] (* Robert G. Wilson v, Feb 14 2017 *)
Table[Mod[Binomial[2p-1, p-1], p^5], {p, Prime[Range[30]]}] (* Harvey P. Dale, Jul 07 2022 *)
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PROG
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(PARI) a(n) = my(p=prime(n)); lift(Mod(binomial(2*p-1, p-1), p^5))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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