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A007749 Numbers n such that n!! - 1 is prime. 49
3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, 728, 842, 888, 2328, 3326, 6404, 8670, 9682, 27056, 44318 (list; graph; refs; listen; history; text; internal format)
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 n such that n!*2^n - 1 is prime. Corresponding primes of the form n!!-1 are listed in A117141[n] = {2,7,47,383,10321919,51011754393599,...}. - Alexander Adamchuk, Nov 19 2006

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The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.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..22.

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

FORMULA

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

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. A091415 = numbers n such that n!*2^n - 1 is prime. Cf. A117141 = Primes of the form n!! - 1.

Sequence in context: A025073 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

STATUS

approved

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Last modified July 29 21:54 EDT 2014. Contains 245046 sequences.