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A291351 Numbers k such that k!4 + 2^10 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

%I A291351 #9 Feb 08 2025 14:29:29
%S A291351 9,13,23,27,33,47,61,113,145,161,191,281,291,417,869,919,1213,1297,
%T A291351 1663,2103,2297,2325,3241,3895,4337,6645,7911,8737,13369,13555,19245,
%U A291351 34025,47779,48589,54521,91355
%N A291351 Numbers k such that k!4 + 2^10 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C A291351 Corresponding primes are: 1069, 1609, 1515229, 40884559, 4996617649, ...
%C A291351 a(37) > 10^5.
%C A291351 Terms > 33 correspond to probable primes.
%H A291351 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n%214%2B4&amp;action=Search">PRP Records. Search for n!4+1024.</a>
%H A291351 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 A291351 OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%e A291351 13!4 + 2^10 = 13*9*5*1 + 1024 = 1609 is prime, so 13 is in the sequence.
%t A291351 MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
%t A291351 Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^10] &]
%t A291351 Select[Range[10^3],PrimeQ[Times@@Range[#,1,-4]+2^10]&] (* The program generates the first 16 terms of the sequence. *) (* _Harvey P. Dale_, Feb 08 2025 *)
%Y A291351 Cf. A007662, A037082, A084438, A123910, A242994.
%K A291351 nonn,more
%O A291351 1,1
%A A291351 _Robert Price_, Aug 22 2017
%E A291351 a(36)-a(37) from _Robert Price_, Sep 25 2019