This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217648 #11 Mar 30 2025 15:27:11
%S A217648 3,3,5,7,37,3889,58321,8377601,22044961,11154675863339008001,
%T A217648 4960821503667767721984001,26284943176784413780354966093824000001,
%U A217648 9847302066569247971143106634078785893903902965760000001,35900221830120178462218744565190401129929679752455520256000000001
%N A217648 Primes of the form 2*k!!! + 1.
%C A217648 k!!! is a triple factorial number (see the definition in A007661).
%C A217648 The corresponding k are in A217647.
%e A217648 2*0!!! + 1 = 2*1 + 1 = 3 ;
%e A217648 2*1!!! + 1 = 2*1 + 1 = 3 ;
%e A217648 2*2!!! + 1 = 2*2 + 1 = 5 ;
%e A217648 2*3!!! + 1 = 2*3 + 1 = 7 ;
%e A217648 2*6!!! + 1 = 2*18 + 1 = 37.
%p A217648 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 A217648 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]
%t A217648 Select[Table[2*Times@@Range[n,1,-3]+1,{n,0,150}],PrimeQ] (* _Harvey P. Dale_, Mar 30 2025 *)
%Y A217648 Cf. A007661, A217647.
%K A217648 nonn
%O A217648 1,1
%A A217648 _Michel Lagneau_, Oct 09 2012