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