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 A227078 The Ramanujan-Nagell squares: A038198(n)^2. 7
 1, 9, 25, 121, 32761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008. L. J. Mordell, Diophantine Equations, Academic Press, NY, 1969, p. 205. LINKS Curtis Bright, Solving Ramanujan's Square Equation Computationally Eric Weisstein's World of Mathematics, Ramanujan's Square Equation FORMULA a(n) + 7 = 2^A060728(n). (a(n) - 1)/8 = A076046(n). CROSSREFS Cf. A060728, A076046, A180445, A227078, A215795. Sequence in context: A092769 A263951 A139818 * A146365 A146373 A084605 Adjacent sequences:  A227075 A227076 A227077 * A227079 A227080 A227081 KEYWORD nonn,fini,full AUTHOR Raphie Frank, Jun 30 2013 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)