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 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 (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 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 - Giovanni Resta, Apr 22 2016 REFERENCES The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.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!<

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Last modified November 30 02:35 EST 2023. Contains 367452 sequences. (Running on oeis4.)