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A007749
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Numbers k such that k!! - 1 is prime.
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61
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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
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1,1
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COMMENTS
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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
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REFERENCES
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The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.
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LINKS
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FORMULA
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MAPLE
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select(t -> isprime(doublefactorial(t)-1), [3, seq(n, n=4..3000, 2)]); # Robert Israel, Apr 21 2016
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MATHEMATICA
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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 *)
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PROG
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(PARI) print1(3); for(n=2, 1e3, if(ispseudoprime(n!<<n-1), print1(", ", 2*n))) \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
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Cf. A091415 (n such that n!*2^n - 1 is prime), A117141 (primes of the form n!! - 1).
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KEYWORD
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nonn,hard,nice
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AUTHOR
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EXTENSIONS
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Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
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STATUS
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approved
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