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%I #8 Sep 25 2019 15:03:30
%S 1,7,11,31,57,73,97,105,209,245,403,545,917,953,1177,1239,1283,1627,
%T 2465,3701,4479,4637,6349,7983,11155,13595,15547,17031,17609,24087,
%U 24707,39773,40407,63329
%N Numbers k such that k!4 + 2^8 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C Corresponding primes are: 257, 277, 487, 1267389841, ...
%C a(35) > 10^5.
%C Terms > 31 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+256.</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!4 + 2^8 = 11*7*3*1 + 256 = 487 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[#, 4] + 2^8] &]
%Y Cf. A007662, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,2
%A _Robert Price_, Aug 22 2017
%E a(34) from _Robert Price_, Sep 25 2019
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