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%I #32 Nov 29 2018 17:21:53
%S 5,6,8,10,68,82,92,98,118,286,796,878,1360,1502,1516,1568,1646,3628,
%T 3716,4048,7982,12776,18070,20594,29902,39632,52988,53864,55610,67448,
%U 85402,89762
%N Numbers k such that k!6 - 3 is prime, where k!6 is the sextuple factorial number (A085158).
%C Corresponding primes are: 2, 3, 13, 37, 73569236156415997, ...
%C a(33) > 10^5.
%C Terms > 10 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6-3&action=Search">PRP Records. Search for n!6-3.</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>
%e 10!6 - 3 = 10*4 - 3 = 37 is prime, so 10 is in the sequence.
%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t Select[Range[4, 50000], PrimeQ[MultiFactorial[#, 6] - 3] &]
%Y Cf. A007661, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Jul 07 2017
%E a(27)-a(32) from _Robert Price_, Aug 03 2018
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