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 A226699 Solutions x of the Pell equation x^2 - 61*y^2 = +4. 1
 2, 1523, 2319527, 3532638098, 5380205503727, 8194049449538123, 12479531931441057602, 19006318937535281189723, 28946611262334301810890527, 44085669946216204122705082898, 67142446381476016544578030363127 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS x = a(n) and y' = b(n) := A226700(n) are the improper and proper nonnegative solutions x^2 - 61*(3*5*13*y')^2 = +4. REFERENCES T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1964, ch. Vi, 58., p. 204-212. LINKS Table of n, a(n) for n=0..10. Index entries for sequences related to Chebyshev polynomials. Index entries for linear recurrences with constant coefficients, signature (1523,-1). FORMULA a(n) = 2*S(n,1523) - 1523*S(n-1,1523), n >= 0, with the Chebyshev S-polynomials (A049310). O.g.f.: (2- 1523*x)/(1- 1523*x + x^2). a(n) = 1523*a(n-1) - a(n-2), n >= 1, a(-1) = 1523, a(0) = 2. EXAMPLE n=0: 2^2 - 0 = +4 (improper), n=1: 1523^2 - 61*(3*5*13*1)^2 = +4, n=2: 2319527^2 - 61*(3*5*13*1523)^2 = +4. CROSSREFS A226700. Sequence in context: A058423 A233906 A329775 * A110027 A179866 A296362 Adjacent sequences: A226696 A226697 A226698 * A226700 A226701 A226702 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 27 2013 STATUS approved

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Last modified July 15 23:38 EDT 2024. Contains 374343 sequences. (Running on oeis4.)