A260297 -id:A260297 - cp's OEIS frontend

A260298 Primes p such that hyperfactorial(p-1) == 1 (mod p).

2, 3, 7, 47, 59, 79, 83, 103, 107, 127, 139, 191, 199, 211, 251, 263, 283, 307, 331, 367, 379, 383, 431, 467, 479, 499, 503, 547, 587, 599, 607, 631, 643, 659, 727, 743, 811, 823, 827, 839, 859, 863, 883, 887, 907, 971, 991, 1087, 1151, 1163, 1171, 1259, 1283

Offset: 1

Matthew Campbell, Jul 22 2015

nonn

Does this contain 2 and the entries of A129518? - R. J. Mathar, Aug 07 2015

Primes p such that (p-1)!! == -1 (mod p). - Thomas Ordowski, Jul 26 2016

Matthew Campbell and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2516 terms from Campbell)

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

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

is(p)=prod(k=2, p-1, Mod(k, p)^k)==1 && isprime(p) \\ Charles R Greathouse IV, Aug 05 2015

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

A260299 Numbers k such that hyperfactorial(prime(k)-1) == 1 (mod prime(k)).

Original entry on oeis.org

1, 2, 4, 15, 17, 22, 23, 27, 28, 31, 34, 43, 46, 47, 54, 56, 61, 63, 67, 73, 75, 76, 83, 91, 92, 95, 96, 101, 107, 109, 111, 115, 117, 120, 129, 132, 141, 143, 144, 146, 149, 150, 153, 154, 155, 164, 167, 181, 190, 192, 193, 205, 208, 214, 215, 219, 224, 225

Offset: 1

Matthew Campbell, Jul 22 2015

nonn

			The 4th prime is 7, and the hyperfactorial of 7 is 4031078400000, which is congruent to 1 mod 7. - _Kellen Myers_, Aug 19 2015

Matthew Campbell and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2516 terms from Campbell)

Cf. A000040, A002109, A260178, A260297, A260298.

PrimePi[fQ[n_]:= Mod[Hyperfactorial[n - 1], n] == 1; Select[Prime@Range@250, fQ]] (* Vincenzo Librandi, Aug 20 2015 *)

is(n,p=prime(n))=prod(k=2,p-1,Mod(k,p)^k)==1 \\ Charles R Greathouse IV, Aug 29 2015

a(n) = pi(A260298(n)).

cp's OEIS Frontend

A260298 Primes p such that hyperfactorial(p-1) == 1 (mod p).

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