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Numbers n such that n!3 - 3^6 is prime.
1

%I #12 Sep 27 2014 06:17:32

%S 11,26,37,38,40,41,62,131,211,212,251,272,284,383,427,538,590,860,

%T 1087,1280,1826,1835,1895,2276,2524,2872,3769,3878,4334,5704,14332,

%U 23386,42694

%N Numbers n such that n!3 - 3^6 is prime.

%C Large terms correspond to probable primes.

%C a(34) > 50000.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-729&amp;action=Search">PRP Records. Search for n!3-729</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="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial</a>

%e 11!3-729 = 11*8*5*2-729= 151 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 lst={};Do[If[PrimeQ[MultiFactorial[n, 3] - 729], AppendTo[lst, n]], {n, 100}];lst

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

%K nonn,more

%O 1,1

%A _Robert Price_, Sep 17 2014