A217650 Numbers k such that 2*k!!! - 1 is prime.

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, 9739, 11569, 14103

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..28.

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

a(26)-a(28) from Michael S. Branicky, Jul 25 2024

Status

approved