%I #13 Sep 27 2014 12:42:00
%S 4,5,7,8,10,11,14,17,35,41,50,59,89,136,164,205,224,283,763,1034,1253,
%T 1630,1820,3199,3800,5080,6124,17306,17398,20768,34033,43607
%N Numbers n such that n!3 + 3^6 is prime.
%C Large terms correspond to probable primes.
%C a(33) > 50000.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+729&action=Search">PRP Records. Search for n!3+729</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 11!3+729 = 11*8*5*2+729 = 1609 is prime, so 11 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] + 729], AppendTo[lst, n]], {n, 100}];lst
%Y Cf. A007661, A037082, A084438, A243078.
%K nonn,more
%O 1,1
%A _Robert Price_, Sep 17 2014