This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227078 #20 Feb 16 2025 08:33:20
%S A227078 1,9,25,121,32761
%N A227078 The Ramanujan-Nagell squares: A038198(n)^2.
%C A227078 a(n) = (2*x - 1)^2 = (sqrt(2)*sqrt(sqrt(6*y^2 - 5) + 1) - 1)^2 = 2^(z + 3) - 7 for x, y, z are the solutions to two Diophantine equations noted by _R. K. Guy_: 2*x^2*(x^2 - 1) = 3*(y^2 - 1) & x*(x - 1)/2 = 2^z - 1 (see A180445). x = {1, 2, 3, 6, 91} = A180445(n), y = {1, 3, 7, 29, 6761} = A227077(n), and z = {0, 1, 2, 4, 12} = A215795(n).
%D A227078 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008.
%D A227078 L. J. Mordell, Diophantine Equations, Academic Press, NY, 1969, p. 205.
%H A227078 Curtis Bright, <a href="https://cs.uwaterloo.ca/~cbright/reports/ramanujans-square-equation.pdf">Solving Ramanujan's Square Equation Computationally</a>
%H A227078 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujansSquareEquation.html">Ramanujan's Square Equation</a>
%F A227078 a(n) + 7 = 2^A060728(n).
%F A227078 (a(n) - 1)/8 = A076046(n).
%Y A227078 Cf. A060728, A076046, A180445, A227077, A215795.
%K A227078 nonn,fini,full
%O A227078 0,2
%A A227078 _Raphie Frank_, Jun 30 2013