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A282410 a(n) = binomial(2*p-1, p-1) modulo p^5, where p = prime(n). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
C. Aebi and G. Cairns, Wolstenholme again, arXiv:1502.05750 [math.NT], 2015.
R. J. McIntosh, On the converse of Wolstenholme's theorem, Acta Arithmetica, Vol. 71, No. 4 (1995), 381-389.
MATHEMATICA
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 *)
PROG
(PARI) a(n) = my(p=prime(n)); lift(Mod(binomial(2*p-1, p-1), p^5))
CROSSREFS
Sequence in context: A333430 A205389 A242473 * A290059 A062006 A199036
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Feb 14 2017
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)