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%I #4 Jun 09 2017 19:43:35
%S 1,5,11,13,17,19,23,31,37,41,49,83,115,161,205,617,683,769,799,1117,
%T 1151,1685,1697,1951,2173,3619,3647,6229,6463,6613,9827,12985,15721,
%U 16933,22579,25181,38869,48755
%N Numbers k such that k!6 + 18 is prime, where k!6 is the sextuple factorial number (A085158 ).
%C Corresponding primes are: 19, 23, 73, 109, 953, 1747, 21523, 1339993, 49579093, 894930593, ...
%C a(39) > 50000.
%C Terms > 49 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+18&action=Search">PRP Records. Search for n!6+18.</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 11!6 + 18 = 11*5 + 18 = 73 is prime, so 11 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] + 18] &]
%Y Cf. A007661, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,2
%A _Robert Price_, Jun 09 2017