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%I #9 Oct 29 2022 12:17:32
%S 3,5,7,9,11,13,19,23,25,33,39,41,63,67,71,85,87,91,133,171,243,291,
%T 1239,1543,1879,2169,2421,3149,3323,3377,3501,3529,5433,5599,7299,
%U 11227,11275,13939,27147,32435,86455,92105
%N Numbers k such that k!4 + 2^3 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C Corresponding primes are: 11, 13, 29, 53, 239, 593, 65843, 1514213, 5221133, ...
%C a(43) > 10^5.
%C Terms > 33 correspond to probable primes.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n%214%2B4&action=Search">PRP Records. Search for n!4+8.</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 13!4 + 2^3 = 13*9*5*1 + 8 = 593 is prime, so 13 is in the sequence.
%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^3] &]
%t Select[Range[100000],PrimeQ[Times@@Range[#,1,-4]+8]&] (* _Harvey P. Dale_, Oct 29 2022 *)
%Y Cf. A007662, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Aug 22 2017
%E a(41)-a(42) from _Robert Price_, Sep 25 2019
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