A217648 Primes of the form 2*k!!! + 1.

3, 3, 5, 7, 37, 3889, 58321, 8377601, 22044961, 11154675863339008001, 4960821503667767721984001, 26284943176784413780354966093824000001, 9847302066569247971143106634078785893903902965760000001, 35900221830120178462218744565190401129929679752455520256000000001

Offset: 1

Author

Michel Lagneau, Oct 09 2012

Keywords

• nonn

Comments

k!!! is a triple factorial number (see the definition in A007661).

The corresponding k are in A217647.

Examples

			2*0!!! + 1 = 2*1 + 1 = 3 ;
2*1!!! + 1 = 2*1 + 1 = 3 ;
2*2!!! + 1 = 2*2 + 1 = 5 ;
2*3!!! + 1 = 2*3 + 1 = 7 ;
2*6!!! + 1 = 2*18 + 1 = 37.
		

Crossrefs

Cf. A007661, A217647.

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, `,2*A(p)+1):else fi:od:

Mathematica

multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Select[Table[2*multiFactorial[n, 3] + 1, {n, 0, 60}], PrimeQ]
Select[Table[2*Times@@Range[n,1,-3]+1,{n,0,150}],PrimeQ] (* Harvey P. Dale, Mar 30 2025 *)