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 A217650 Numbers k such that 2*k!!! - 1 is prime. 3
 2, 3, 4, 5, 11, 23, 27, 29, 36, 40, 41, 71, 89, 119, 127, 157, 163, 187, 652, 1374, 1518, 2922, 5193, 6663, 7455 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS k!!! is a triple factorial, see the definition in A007661. LINKS EXAMPLE 5 is in the sequence because 2*5!!! - 1 = 2*10 - 1 = 19 is prime. MAPLE A:= n -> mul(k, k = select(k -> k mod 3 = n mod 3, [\$1 .. n])): for p from 0 to 200 do:if type(2*A(p)-1, prime)=true then printf(`%d, `, p):else fi:od: MATHEMATICA lst={}; multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Do[If[PrimeQ[2*multiFactorial[n, 3] - 1], AppendTo[lst, n]], {n, 0, 1000}]; lst PROG (PARI) is(n)=ispseudoprime(2*prod(i=0, (n-2)\3, n-3*i)-1) \\ Charles R Greathouse IV, Oct 09 2012 (PFGW) ABC2 2*\$a!3-1 a: from 1 to 6000 Charles R Greathouse IV, Oct 09 2012 CROSSREFS Cf. A007661, A217647, A217650. Sequence in context: A123823 A274837 A064959 * A032988 A280206 A190783 Adjacent sequences:  A217647 A217648 A217649 * A217651 A217652 A217653 KEYWORD nonn,hard,more AUTHOR Michel Lagneau, Oct 09 2012 EXTENSIONS a(20)-a(23) from Charles R Greathouse IV, Oct 09 2012 a(24)-a(25) from Jinyuan Wang, May 15 2021 STATUS approved

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Last modified July 3 18:04 EDT 2022. Contains 355055 sequences. (Running on oeis4.)