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%I #41 Apr 03 2023 10:36:10
%S 0,1,3,5,7,9,21,23,27,57,75,103,169,219,245,461,695,1169,3597,3637,
%T 7495,27743,28799,32501
%N Numbers n such that n!! + 2 is prime.
%C a(25) > 50000. - _Robert Price_, Jan 18 2015
%C a(1)=0 since 0!!=1 and 1+2 = 3 is prime. - _Robert Price_, Jan 18 2015
%H C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php/MultifactorialPrime.html">Multifactorial prime</a>
%H C. Caldwell and H. Dubner (Eds): <a href="https://t5k.org/lists/top_ten/">The top ten prime numbers: from the unpublished collections of R. Ondrejka</a> (May 2001), Table 21 F, p. 75
%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</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 The OpenPFGW Project, <a href="http://sourceforge.net/projects/openpfgw/">Primality Tester</a>
%t lst={};Do[If[PrimeQ[n!!+2], AppendTo[lst, n]], {n, 0, 13^3}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 08 2008 *)
%t Select[Range[0,33000],PrimeQ[#!!+2]&] (* _Harvey P. Dale_, Jul 28 2017 *)
%Y Cf. A006882, A080778 and A076186, A076188, A076189, A076190, A076193, A076194, A076195, A076196, A076197 for other values of s in n!! + 2^s.
%K nonn,more
%O 1,3
%A _Zak Seidov_, Nov 02 2002
%E Edited and extended (n<4096) by _Hugo Pfoertner_, Jun 19 2003
%E One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 30 2007
%E a(22) - a(23) from _Robert Price_, Oct 17 2012
%E a(24) from _Robert Price_, Jan 18 2015