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
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Feb 14 2017
STATUS
approved