A117141 Primes of the form n!! - 1.

2, 7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999

Offset

1,1

References

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 158.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..15

Formula

a(n) = A093173(n-1) for n > 1. - Alexander Adamchuk, Apr 18 2007

a(n) = A006882(A007749(n)) - 1. - Elmo R. Oliveira, Feb 22 2025

Example

6!! - 1 = 6*4*2 - 1 = 48 - 1 = 47, which is prime.
8!! - 1 = 8*6*4*2 - 1 = 384 - 1 = 383, which is prime.

Maple

SFACT:= proc(n) local i, j, k; for k from 1 by 1 to n do i:=k; j:=k-2; while j >0 do i:=i*j; j:=j-2; od: if isprime(i-1) then print(i-1); fi; od: end: SFACT(100);

Mathematica

lst={}; Do[p=n!!-1; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)
Select[Table[n!!-1, {n, 1, 100}], PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)

Prog

(PARI) print1(2); for(n=1, 1e3, if(ispseudoprime(t=n!<<n-1), print1(", "t))) \\ Charles R Greathouse IV, Jun 16 2011

Crossrefs

Cf. A002981, A002982, A006882, A007749, A088332.

Cf. A093173 = primes of the form (2^n * n!) - 1.

Sequence in context: A091117 A056854 A330149 * A349965 A305533 A125813

Adjacent sequences: A117138 A117139 A117140 * A117142 A117143 A117144

Keyword

nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 21 2006

Status

approved