Voozh

A217647

Numbers k such that 2*k!!! + 1 is prime.

0, 1, 2, 3, 6, 12, 15, 20, 21, 44, 54, 75, 102, 116, 182, 288, 326, 344, 357, 458, 1296, 2394, 2913, 4749, 6834, 10425, 17448

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OFFSET

1,3

COMMENTS

k!!! is a triple factorial, see the definition in A007661.

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

6 is in the sequence because 2*6!!! + 1 = 2*18 + 1 = 37 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

Select[Range[0, 5000], PrimeQ[2*Times@@Range[#, 1, -3]+1]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Nov 26 2025 *)

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 5000

Charles R Greathouse IV, Oct 09 2012

CROSSREFS

Cf. A007661, A217648, A217650.

Sequence in context: A252792 A284638 A111271 * A070926 A226023 A124485

Adjacent sequences: A217644 A217645 A217646 * A217648 A217649 A217650

KEYWORD

nonn,hard,more