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%I #7 Sep 25 2019 14:47:10
%S 0,1,3,7,9,13,19,27,35,37,65,67,75,83,89,101,111,229,363,633,1605,
%T 1663,1769,1863,1947,2695,3003,5309,7835,9495,9945,11041,18833,21119,
%U 21465,21889,24509,26757,27595,33657,54007,67699,87915
%N Numbers k such that k!4 + 2^4 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C Corresponding primes are: 17, 17, 19, 37, 61, 601, 65851, 40883551, ...
%C a(44) > 10^5.
%C Terms > 37 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+16.</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 + 2^4 = 13*9*5*1 + 16 = 601 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] + 2^4] &]
%Y Cf. A007662, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,3
%A _Robert Price_, Aug 22 2017
%E a(41)-a(43) from _Robert Price_, Sep 25 2019
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