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A243078 Numbers k such that k!3 - 3^2 is prime, where k!3 = k!!! is a triple factorial number (A007661).

%I A243078 #43 Mar 12 2023 08:48:47
%S A243078 7,8,10,13,16,17,20,23,28,29,32,43,46,47,53,56,59,61,76,95,107,139,
%T A243078 148,218,349,764,1009,1130,1183,1429,1516,2072,2471,4937,10204,13993,
%U A243078 16249,18166,25733,29033,40090
%N A243078 Numbers k such that k!3 - 3^2 is prime, where k!3 = k!!! is a triple factorial number (A007661).
%C A243078 a(42) > 50000.
%C A243078 k=2 and k=4 produce values (-7 and -5) whose absolute value is a prime.
%C A243078 Terms > 2000 correspond to probable primes.
%H A243078 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-9&amp;action=Search">PRP Records. Search for n!3-9.</a>
%H A243078 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A243078 17!3 - 3^2 = 17*14*11*8*5*2 - 9 = 209431 is prime, so 17 is in the sequence. - _Jens Kruse Andersen_, Aug 20 2014
%t A243078 MultiFactorial[n_,k_]:=If[n<1,1,If[n<k+1,n,n*MultiFactorial[n-k,k]]];
%t A243078 lst={}; Do[If[PrimeQ[MultiFactorial[n,3]-3^2],AppendTo[lst,n]],{n,50000}]; lst
%Y A243078 Cf. A007661, A037082, A084438, A123910, A242994.
%K A243078 nonn,more
%O A243078 1,1
%A A243078 _Robert Price_, May 30 2014
%E A243078 a(41) from _Robert Price_, Sep 19 2014