|
%I #19 Mar 16 2023 10:14:33
%S 8,11,13,22,29,49,56,61,103,142,149,257,319,365,680,736,737,749,947,
%T 974,1040,4277,4678,9961,10652,15545,18064,31325,34918,41032
%N Numbers n such that n!3 - 3^3 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C Large terms correspond to probable primes.
%C a(31) > 50000.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-27&action=Search">PRP Records. Search for n!3-27</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!3-27 = 11*8*5*2-27 = 853 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] - 27], AppendTo[lst, n]], {n, 100}];lst
%t Select[Range[6,1100],PrimeQ[Times@@Range[#,1,-3]-27]&] (* _Harvey P. Dale_, Mar 16 2023 *)
%Y Cf. A007661, A037082, A084438, A243078.
%K nonn,more
%O 1,1
%A _Robert Price_, Sep 17 2014
|
