A117141 Primes of the form n!! - 1.

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

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 21 2006

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

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

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

Programs

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 *)

PARI

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

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