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

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

Author

Matthew Campbell, Jul 22 2015

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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