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

Offset: 1

Author

Michel Lagneau, Oct 09 2012

Keywords

• nonn
• hard
• more

Comments

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

Examples

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

Crossrefs

Cf. A007661, A217648, A217650.

Programs

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

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

Extensions

a(22)-a(24) from Charles R Greathouse IV, Oct 09 2012

a(25) from Jinyuan Wang, May 15 2021

a(26)-a(27) from Michael S. Branicky, Jul 25 2024