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%I #39 Jan 17 2023 16:50:53
%S 0,1,2,3,4,5,9,10,11,13,24,65,76
%N Numbers k such that (k!)^2 + 1 is prime.
%C a(14) > 780. - _Ralf Stephan_, Oct 21 2002
%C a(14) > 2500. - Gabriel Cunningham (gcasey(AT)mit.edu), Feb 23 2004
%C a(14) > 10000. - _Charles R Greathouse IV_, Nov 16 2006
%C a(14) > 16000. - _Robert Price_, Aug 13 2011
%D H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
%H M. Oakes, <a href="http://groups.yahoo.com/group/primeform/message/10881">Re: Gaussian primorial and factorial primes</a>, Primeform, Dec 21 2010
%H Mike Oakes, Andrew Walker, David Broadhurst, <a href="/A046029/a046029.txt">Gaussian primorial and factorial primes</a>, digest of 7 messages in primeform Yahoo group, Dec 20 - Dec 21, 2010.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Factorial.html">Factorial</a>
%e 9 is a term because (9!)^2 + 1 is prime.
%t Do[ If[ PrimeQ[n!^2 + 1], Print[n]], {n, 500}] (* _Robert G. Wilson v_, Apr 14 2004 *)
%t Select[Range[1000], PrimeQ[(#!^2 + 1)] &] (* _Vincenzo Librandi_, May 28 2015 *)
%o (Magma) [n: n in [0..90] |IsPrime(Factorial(n)^2+1)]; // _Vincenzo Librandi_, May 28 2015
%Y Cf. A020549, A051739.
%K nonn,more,hard
%O 1,3
%A _Eric W. Weisstein_
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