

A007749


Numbers k such that k!!  1 is prime.


61



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
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OFFSET

1,1


COMMENTS

a(n) is even for n>1. a(n) = 2*A091415(n1) 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The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.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



FORMULA



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[f1], 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!<<n1), print1(", ", 2*n))) \\ Charles R Greathouse IV, Jun 16 2011


CROSSREFS

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


KEYWORD

nonn,hard,nice


AUTHOR



EXTENSIONS

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


STATUS

approved



