A217647 - OEIS

%I #16 Jul 26 2024 07:59:47

%S 0,1,2,3,6,12,15,20,21,44,54,75,102,116,182,288,326,344,357,458,1296,

%T 2394,2913,4749,6834,10425,17448

%N Numbers k such that 2*k!!! + 1 is prime.

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

%e 6 is in the sequence because 2*6!!! + 1 = 2*18 + 1 = 37 is prime.

%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, `,p):else fi:od:

%t 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 (PARI) is(n)=ispseudoprime(2*prod(i=0, (n-2)\3, n-3*i)+1) \\ _Charles R Greathouse IV_, Oct 09 2012

%o (PFGW)

%o ABC2 2*$a!3+1

%o a: from 1 to 5000

%o _Charles R Greathouse IV_, Oct 09 2012

%Y Cf. A007661, A217648, A217650.

%K nonn,hard,more

%O 1,3

%A _Michel Lagneau_, Oct 09 2012

%E a(22)-a(24) from _Charles R Greathouse IV_, Oct 09 2012

%E a(25) from _Jinyuan Wang_, May 15 2021

%E a(26)-a(27) from _Michael S. Branicky_, Jul 25 2024