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%I #7 Sep 25 2019 15:04:12
%S 9,13,23,27,33,47,61,113,145,161,191,281,291,417,869,919,1213,1297,
%T 1663,2103,2297,2325,3241,3895,4337,6645,7911,8737,13369,13555,19245,
%U 34025,47779,48589,54521,91355
%N Numbers k such that k!4 + 2^10 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C Corresponding primes are: 1069, 1609, 1515229, 40884559, 4996617649, ...
%C a(37) > 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+1024.</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 + 2^10 = 13*9*5*1 + 1024 = 1609 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] + 2^10] &]
%Y Cf. A007662, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Aug 22 2017
%E a(36)-a(37) from _Robert Price_, Sep 25 2019