A007749 Numbers k such that k!! - 1 is prime.

3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, 728, 842, 888, 2328, 3326, 6404, 8670, 9682, 27056, 44318, 76190, 100654, 145706

Offset

1,1

Comments

a(n) is even for n>1. a(n) = 2*A091415(n-1) for n>1, where A091415(n) = {2, 3, 4, 8, 13, 32, 41, 45, 59, 97, 107, 364, 421, 444, 1164, 1738, 3202, 4335, 4841, ...} (numbers k such that k!*2^k - 1 is prime). Corresponding primes of the form k!!-1 are listed in A117141 = {2, 7, 47, 383, 10321919, 51011754393599, ...}. - Alexander Adamchuk, Nov 19 2006

The PFGW program has been used to certify all the terms up to a(25), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Apr 22 2016

References

The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.

Links

Table of n, a(n) for n=1..25.

Ken Davis, Status of Search for Multifactorial Primes.

Ken Davis, Results for n!2-1.

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations

Index entries for sequences related to factorial numbers

Eric Weisstein's World of Mathematics, Double Factorial Prime

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Formula

a(n) = 2*A091415(n-1) for n>1. - Alexander Adamchuk, Nov 19 2006

Maple

select(t -> isprime(doublefactorial(t)-1), [3, seq(n, n=4..3000, 2)]); # Robert Israel, Apr 21 2016

Mathematica

a(1) = 3, for n>1 k=2; f=2; Do[k=k+2; f=f*k; If[PrimeQ[f-1], Print[k]], {n, 2, 5000}] (* Alexander Adamchuk, Nov 19 2006 *)
Select[Range[45000], PrimeQ[#!!-1]&] (* Harvey P. Dale, Aug 07 2013 *)

Prog

(PARI) print1(3); for(n=2, 1e3, if(ispseudoprime(n!<<n-1), print1(", ", 2*n))) \\ Charles R Greathouse IV, Jun 16 2011

Crossrefs

Cf. A006882.

Cf. A091415 (n such that n!*2^n - 1 is prime), A117141 (primes of the form n!! - 1).

Sequence in context: A325432 A204659 A134580 * A063506 A084438 A186700

Adjacent sequences: A007746 A007747 A007748 * A007750 A007751 A007752

Keyword

nonn,hard,nice

Author

N. J. A. Sloane

Extensions

Entry updated by Robert G. Wilson v, Aug 18 2000

Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008

a(23)-a(24) from Sou Fukui, Jun 05 2015

a(25) from Sou Fukui, Apr 21 2016

Status

approved