|
%I #6 Jan 25 2021 13:49:31
%S 16,17,34,38,49,62,74,97,125,137,146,178,188,235,664,863,916,1988,
%T 2059,2837,5353,5489,7483,9344,12631,13796,17122,23134,30409,33077
%N Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).
%C Corresponding primes are 38557, 189757, 17961239276317, 3091650738156317, ... .
%C a(31) > 50000.
%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n!3-19683&action=Search">PRP Records. Search for n!3-19683.</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>
%e 16!3 - 3^9 = 16*13*10*7*4*1 - 19683 = 58240 - 19683 = 38557 is prime, so 16 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[15, 50000], PrimeQ[MultiFactorial[#, 3] - 3^9] &]
%t Select[Range[12,33100],PrimeQ[Times@@Range[#,1,-3]-19683]&] (* _Harvey P. Dale_, Jan 25 2021 *)
%Y Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145, A265201.
%K hard,more,nonn
%O 1,1
%A _Robert Price_, Jan 09 2016
|
