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%I #7 Oct 28 2014 03:50:10
%S 2,4,5,7,8,10,11,13,14,16,19,20,26,28,29,32,41,56,61,77,100,169,181,
%T 205,338,347,955,1952,2197,2428,2960,3430,4618,7478,8209,8422,9235,
%U 11107,13481,18194,19229,29854,46532
%N Numbers n such that n!3 + 3 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C Large terms correspond to probable primes.
%C a(44) > 50000.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-27&action=Search">PRP Records. Search for n!3-27</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+3 = 11*8*5*2+3 = 883 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] + 3], AppendTo[lst, n]], {n, 100}];lst
%Y Cf. A007661, A037082, A084438, A243078.
%K nonn,more
%O 1,1
%A _Robert Price_, Oct 27 2014