A291345 - OEIS

%I #11 Apr 11 2022 18:07:43

%S 5,7,11,13,19,21,25,27,35,37,51,55,65,71,105,107,129,223,229,273,307,

%T 337,345,479,509,517,519,921,963,993,1309,1697,1855,1871,2451,2573,

%U 2755,3059,3271,4005,4823,17079,20209,20559,37845,38343,68383,79617,81539

%N Numbers k such that k!4 + 2^5 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

%C Corresponding primes are: 37, 53, 263, 617, 65867, 208877, 5221157, 40883567, ...

%C a(50) > 10^5.

%C Terms > 37 correspond to probable primes.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=n%214%2B4&amp;action=Search">PRP Records. Search for n!4+32.</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 13!4 + 2^5 = 13*9*5*1 + 32 = 617 is prime, so 13 is in the sequence.

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

%t Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^5] &]

%t Select[Range[82000],PrimeQ[Times@@Range[#,1,-4]+32]&] (* _Harvey P. Dale_, Apr 11 2022 *)

%Y Cf. A007662, A037082, A084438, A123910, A242994.

%K nonn,more

%O 1,1

%A _Robert Price_, Aug 22 2017

%E a(47)-a(49) from _Robert Price_, Sep 25 2019