%I #9 Dec 03 2015 04:48:04

%S 2,4,7,11,25,38,47,94,95,155,275,277,292,299,395,409,614,1409,1963,

%T 3422,5243,5884,5971,8527,10882,13223,16406,20851,28886

%N Numbers n such that n!3 + 3^10 is prime, where n!3 = n!!! is a triple factorial number (A007661).

%C Corresponding primes are: 59051, 59053, 59077, 59929, 608667049, 3091650738235049, 262134882788466747049, ...

%C a(30) > 50000.

%C Terms > 47 correspond to probable primes.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3+59049&amp;action=Search">PRP Records. Search for n!3+59049.</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!3 + 3^10 = 11*8*5*2 + 59049 = 59929 is prime, so 11 is in the sequence.

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

%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 3] + 3^10] &]

%o (PARI) for(n=1, 1e3, if(ispseudoprime(prod(i=0, floor((n-1)/3), n-3*i) + 3^10), print1(n, ", "))) \\ _Altug Alkan_, Nov 18 2015

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

%K nonn,more

%O 1,1

%A _Robert Price_, Nov 18 2015