|
| |
|
|
A007749
|
|
Numbers n such that n!! - 1 is prime.
|
|
50
| |
|
|
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; 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 (alex(AT)kolmogorov.com), 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| The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.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
| 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 (alex(AT)kolmogorov.com), 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 (alex(AT)kolmogorov.com), Nov 19 2006
|
|
|
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 * A139452 A063506 A084438
Adjacent sequences: A007746 A007747 A007748 * A007750 A007751 A007752
|
|
|
KEYWORD
| nonn,hard,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Entry updated by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 18 2000
Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
|
| |
|
|
