A291350 - OEIS

%I #7 Sep 25 2019 15:03:02

%S 9,11,13,17,19,21,29,31,33,35,67,103,111,129,179,355,713,799,921,1013,

%T 1389,1543,2097,2287,3657,4115,7031,10689,11715,16401,16893,19497,

%U 29737,35615

%N Numbers k such that k!4 + 2^9 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

%C Corresponding primes are: 557, 743, 1097, 10457, 66347, 209357, 151413137, ...

%C a(35) > 10^5.

%C Terms > 35 correspond to probable primes.

%H 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+512.</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 + 2^9 = 11*7*3*1 + 512 = 743 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] + 2^9] &]

%Y Cf. A007662, A037082, A084438, A123910, A242994.

%K nonn,more

%O 1,1

%A _Robert Price_, Aug 22 2017