A217648 - OEIS

%I #9 May 16 2021 00:45:45

%S 3,3,5,7,37,3889,58321,8377601,22044961,11154675863339008001,

%T 4960821503667767721984001,26284943176784413780354966093824000001,

%U 9847302066569247971143106634078785893903902965760000001,35900221830120178462218744565190401129929679752455520256000000001

%N Primes of the form 2*k!!! + 1.

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

%C The corresponding k are in A217647.

%e 2*0!!! + 1 = 2*1 + 1 = 3 ;

%e 2*1!!! + 1 = 2*1 + 1 = 3 ;

%e 2*2!!! + 1 = 2*2 + 1 = 5 ;

%e 2*3!!! + 1 = 2*3 + 1 = 7 ;

%e 2*6!!! + 1 = 2*18 + 1 = 37.

%p 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:

%t 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]

%Y Cf. A007661, A217647.

%K nonn

%O 1,1

%A _Michel Lagneau_, Oct 09 2012