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%I #10 Sep 27 2014 18:09:53
%S 7,10,11,22,23,25,44,46,47,50,53,55,89,122,214,410,427,526,539,575,
%T 1369,1370,2291,4999,5374,7202,7375,7823,8921,9764,22967,25507,44117
%N Numbers n such that n!3 + 3^5 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C Large terms correspond to probable primes.
%C a(34) > 50000.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+243&action=Search">PRP Records. Search for n!3+243</a>
%H Joe McLean, <a href="http://web.archive.org/web/20091027034731/http://uk.geocities.com/nassarawa%40btinternet.com/probprim2.htm">Interesting Sources of Probable Primes</a>
%H OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a>
%e 10!3+243 = 10*7*4*1+243= 523 is prime, so 10 is in the sequence.
%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] + 243], AppendTo[lst, n]], {n, 100}];lst
%Y Cf. A007661, A037082, A084438, A243078.
%K nonn,more
%O 1,1
%A _Robert Price_, Sep 25 2014