A247465 - OEIS

%I #12 Feb 16 2025 08:33:23

%S 10,19,28,50,67,77,89,112,139,146,184,194,233,310,311,388,886,1139,

%T 1648,1694,2405,2554,3709,4015,5410,5908,6407,8065,9061,9875,11722,

%U 13471,26026,26656,29441,32741

%N Numbers n such that n!3 - 3^5 is prime.

%C Large terms correspond to probable primes.

%C a(37) > 50000.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-243&amp;action=Search">PRP Records. Search for n!3-243</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>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>

%e 10!3-243 = 10*7*4*1-243 = 37 is prime, so 10 is in the sequence.

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

%t lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 243], AppendTo[lst, n]], {n, 100}];lst

%Y Cf. A007661, A037082, A084438, A243078.

%K nonn,more

%O 1,1

%A _Robert Price_, Sep 17 2014