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 A217647 #16 Jul 26 2024 07:59:47
%S A217647 0,1,2,3,6,12,15,20,21,44,54,75,102,116,182,288,326,344,357,458,1296,
%T A217647 2394,2913,4749,6834,10425,17448
%N A217647 Numbers k such that 2*k!!! + 1 is prime.
%C A217647 k!!! is a triple factorial, see the definition in A007661.
%e A217647 6 is in the sequence because 2*6!!! + 1 = 2*18 + 1 = 37 is prime.
%p A217647 A:= n -> mul(k, k = select(k -> k mod 3 = n mod 3, [$1 .. n])): for p from 0 to 200 do:if type(2*A(p)+1,prime)=true then printf(`%d, `,p):else fi:od:
%t A217647 lst={}; multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Do[If[PrimeQ[2*multiFactorial[n, 3] + 1], AppendTo[lst, n]], {n, 0, 1000}]; lst
%o A217647 (PARI) is(n)=ispseudoprime(2*prod(i=0, (n-2)\3, n-3*i)+1) \\ _Charles R Greathouse IV_, Oct 09 2012
%o A217647 (PFGW)
%o A217647 ABC2 2*$a!3+1
%o A217647 a: from 1 to 5000
%o A217647 _Charles R Greathouse IV_, Oct 09 2012
%Y A217647 Cf. A007661, A217648, A217650.
%K A217647 nonn,hard,more
%O A217647 1,3
%A A217647 _Michel Lagneau_, Oct 09 2012
%E A217647 a(22)-a(24) from _Charles R Greathouse IV_, Oct 09 2012
%E A217647 a(25) from _Jinyuan Wang_, May 15 2021
%E A217647 a(26)-a(27) from _Michael S. Branicky_, Jul 25 2024