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%I #15 Sep 03 2023 19:53:08
%S 2,5,11,12,71
%N Numbers n such that there exist x, y with n^2 = x! + y!.
%C a(6) > 10^78. - _Sascha Kurz_, Mar 24 2002
%C a(6) > 10^1545. - _Robert G. Wilson v_, Apr 06 2006
%C a(6) > 10^10000. - _Sean A. Irvine_, Sep 03 2023
%H Lev Emelyanov, <a href="http://forumgeom.fau.edu/POLYA/Inventory/Inventory015.html">Square as sum of two factorials</a>
%e 2^2 = 2!+2!; 5^2 = 4!+1!; 11^2 = 5!+1!; 12^2 = 5!+4!; 71^2 = 7!+1!.
%t Sqrt@ Select[ Sort@ Flatten@ Table[x! + y!, {x, 650}, {y, x}], IntegerQ@ Sqrt@ # &] (* _Robert G. Wilson v_, Apr 06 2006 *)
%K nonn
%O 1,1
%A Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Nov 23 2001
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