|
%I #8 Sep 25 2019 14:53:58
%S 3,9,15,17,19,29,31,45,55,63,73,101,135,173,217,271,439,535,729,787,
%T 933,1473,1651,6617,7805,12461,13253,18627,20243,55271
%N Numbers k such that k!4 + 2^6 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).
%C Corresponding primes are: 67, 109, 3529, 10009, 65899, 151412689, 1267389649, ...
%C a(31) > 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+64.</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 15!4 + 2^6 = 15*11*7*3*1 + 64 = 3529 is prime, so 15 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] + 2^6] &]
%Y Cf. A007662, A037082, A084438, A123910, A242994.
%K nonn,more
%O 1,1
%A _Robert Price_, Aug 22 2017
%E a(30) from _Robert Price_, Sep 25 2019
|
