A260298 -id:A260298 - cp's OEIS frontend

A129518 Numbers k > 2 such that k divides (k-2)!! - 1 and (k-3)!! - 1.

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

Alexander Adamchuk, Apr 18 2007

nonn

All terms are primes of the form 4m+3 belonging to A002145. A002145 is the union of this sequence and A129517 (odd primes p such that p divides (p-1)!! - 1).

Odd numbers k > 1 such that k divides (k-1)!! + 1. - Thomas Ordowski, Jul 26 2016

Cf. A006882 (double factorials).
Cf. A002145 (primes of form 4k+3).
Cf. A129517 (odd primes p such that p divides (p-1)!! - 1).
Cf. A129516 (numbers k such that k divides (k-1)!! - 1).
Cf. A260298.

Select[Range[3,2000],IntegerQ[((#-2)!!-1)/# ]&&IntegerQ[((#-3)!!-1)/# ]&]

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

A129518 Numbers k > 2 such that k divides (k-2)!! - 1 and (k-3)!! - 1.

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

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