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A227078 The Ramanujan-Nagell squares: A038198(n)^2. 7

%I

%S 1,9,25,121,32761

%N The Ramanujan-Nagell squares: A038198(n)^2.

%C 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} = A227078(n), and z = {0, 1, 2, 4, 12} = A215795(n).

%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008.

%D L. J. Mordell, Diophantine Equations, Academic Press, NY, 1969, p. 205.

%H Curtis Bright, <a href="https://cs.uwaterloo.ca/~cbright/reports/ramanujans-square-equation.pdf">Solving Ramanujan's Square Equation Computationally</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujansSquareEquation.html">Ramanujan's Square Equation</a>

%F a(n) + 7 = 2^A060728(n).

%F (a(n) - 1)/8 = A076046(n).

%Y Cf. A060728, A076046, A180445, A227078, A215795.

%K nonn,fini,full

%O 0,2

%A _Raphie Frank_, Jun 30 2013

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Last modified November 18 14:59 EST 2019. Contains 329262 sequences. (Running on oeis4.)