A287844 - OEIS

%I #5 Jun 01 2017 21:10:05

%S 2,4,8,10,14,16,20,22,26,34,70,164,346,398,902,938,1426,1682,1928,

%T 3596,3796,15058,25654,37330

%N Numbers k such that k!6 + 3 is prime, where k!6 is the sextuple factorial number (A085158 ).

%C Corresponding primes are: 5, 7, 19, 43, 227, 643, 4483, 14083, 116483, 13404163, ...

%C a(25) > 50000.

%C Terms > 34 correspond to probable primes.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!6+3&amp;action=Search">PRP Records. Search for n!6+3.</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 10!6 + 3 = 10*4 + 3 = 43 is prime, so 10 is in the sequence.

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

%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 6] + 3] &]

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

%K nonn,more

%O 1,1

%A _Robert Price_, Jun 01 2017