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%I #14 Aug 11 2019 10:33:04
%S 1,3,7,29,6761
%N y solutions to the Diophantine equation 2*x^2*(x^2 - 1) = 3*(y^2 - 1)
%C Also solutions to (2*x^2 - 1)^2 = 6*y^2 - 5 as outlined in A180445, which gives the x solutions to this equation {1, 2, 3, 6, 91}.
%C (sqrt(2)*sqrt(sqrt(6*a(n)^2 - 5) + 1) - 1)^2 = A038198(n)^2 gives the Ramanujan-Nagell squares listed in A227078.
%H Richard K. Guy, <a href="http://www.jstor.org/stable/2322249">The Strong Law of Small Numbers</a> (example #29).
%t Select[Table[Sqrt[3-2x^2+2x^4]/Sqrt[3],{x,0,100}],IntegerQ]//Union (* _Harvey P. Dale_, Aug 11 2019 *)
%Y Cf. A180445, A038198, A227078.
%K nonn
%O 0,2
%A _Raphie Frank_, Jun 30 2013