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%I #4 Jun 09 2017 19:43:57
%S 5,9,17,21,29,53,57,105,111,279,303,435,483,677,1049,1217,1395,9651,
%T 26031,31937
%N Numbers k such that k!6 + 32 is prime, where k!6 is the sextuple factorial number (A085158 ).
%C Corresponding primes are: 37, 59, 967, 8537, 623677, 2229272062357, 38661097149707, ...
%C a(21) > 50000.
%C Terms > 29 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+32&action=Search">PRP Records. Search for n!6+32.</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 17!6 + 32 = 17*11*5 + 32 = 967 is prime, so 17 is in the sequence.
%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 32] &]
%Y Cf. A007661, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Jun 09 2017
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