A289699 - OEIS

%I #14 Nov 29 2018 16:21:28

%S 11,13,15,19,33,35,39,59,63,75,105,143,187,213,271,307,431,549,1211,

%T 1597,1879,2025,3085,5995,5997,6697,6795,10543,21515,25811,34345,

%U 57561,70797,71671

%N Numbers k such that k!6 - 32 is prime, where k!6 is the sextuple factorial number (A085158).

%C Corresponding primes are: 23, 59, 373, 1697, 7577923, 21827543, 295540213, ...

%C a(35) > 10^5.

%C Terms > 39 correspond to probable primes.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6-32&amp;action=Search">PRP Records. Search for n!6-32.</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!6 - 32 = 15*9*3 - 32 = 373 is prime, so 15 is in the sequence.

%t MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];

%t Select[Range[10, 50000], PrimeQ[MultiFactorial[#, 6] - 32] &]

%Y Cf. A007661, A037082, A084438, A123910, A242994.

%K nonn,more

%O 1,1

%A _Robert Price_, Jul 09 2017

%E a(32)-a(34) from _Robert Price_, Aug 04 2018