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%I #13 Sep 27 2014 01:56:06
%S 10,13,14,17,20,26,29,31,32,50,59,77,82,104,164,185,217,263,293,361,
%T 437,442,545,547,599,608,623,739,782,1081,1120,1138,1429,2516,2518,
%U 4277,4529,5438,5596,11945,12716,13955,14540,31730,31769,42964,46396
%N Numbers n such that n!!! - 3^4 is prime.
%C Large terms correspond to probable primes.
%C a(48) > 50000.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-81&action=Search">PRP Records. Search for n!3-81</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!3-81 = 10*7*4*1-81 = 199 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] - 81], AppendTo[lst, n]], {n, 100}];lst
%Y Cf. A007661, A037082, A084438, A243078.
%K nonn,more
%O 1,1
%A _Robert Price_, Sep 17 2014
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