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Primes p such that hyperfactorial(p-1) == 1 (mod p).
3

%I #38 Aug 27 2016 10:18:29

%S 2,3,7,47,59,79,83,103,107,127,139,191,199,211,251,263,283,307,331,

%T 367,379,383,431,467,479,499,503,547,587,599,607,631,643,659,727,743,

%U 811,823,827,839,859,863,883,887,907,971,991,1087,1151,1163,1171,1259,1283

%N Primes p such that hyperfactorial(p-1) == 1 (mod p).

%C Does this contain 2 and the entries of A129518? - _R. J. Mathar_, Aug 07 2015

%C Primes p such that (p-1)!! == -1 (mod p). - _Thomas Ordowski_, Jul 26 2016

%H Matthew Campbell and Charles R Greathouse IV, <a href="/A260298/b260298.txt">Table of n, a(n) for n = 1..10000</a> (first 2516 terms from Campbell)

%F a(n) = prime(A260299(n)).

%t fQ[n_] := Mod[Hyperfactorial[n - 1], n] == 1; Select[ Prime@ Range@ 210, fQ] (* _Robert G. Wilson v_, Aug 06 2015 *)

%o (PARI) is(p)=prod(k=2, p-1, Mod(k, p)^k)==1 && isprime(p) \\ _Charles R Greathouse IV_, Aug 05 2015

%Y Cf. A000040, A002109, A129518, A260178, A260297, A260299.

%K nonn

%O 1,1

%A _Matthew Campbell_, Jul 22 2015