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%I #6 Aug 10 2021 13:21:26
%S 2,4,8,10,14,20,22,26,32,40,110,116,142,148,200,370,854,1166,1594,
%T 2164,4424,5942,9086,13300,15224,20482,22940,27478,47486
%N Numbers k such that k!6 + 27 is prime, where k!6 is the sextuple factorial number (A085158 ).
%C Corresponding primes are: 29, 31, 43, 67, 251, 4507, 14107, 116507, 3727387, 536166427, ...
%C a(30) > 50000.
%C Terms > 40 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+27&action=Search">PRP Records. Search for n!6+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>
%e 10!6 + 27 = 10*4 + 27 = 67 is prime, so 10 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] + 27] &]
%t Select[Range[48000],PrimeQ[Times@@Range[#,1,-6]+27]&] (* _Harvey P. Dale_, Aug 10 2021 *)
%Y Cf. A007661, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Jun 09 2017