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 A225204 Numerators of convergents to the square root of the golden ratio. 7
 1, 4, 5, 14, 159, 491, 2614, 3105, 33664, 36769, 107202, 572779, 1825539, 9700474, 11526013, 32752500, 142536013, 175288513, 317824526, 810937565, 3561574786, 182451251651, 186012826437, 926502557399, 2039017941235, 5004538439869, 157179709577174 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..26. I. J. Good, Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio (Condensed Version), Journal of the Operational Research Society, 43 (1992), 837-842. I. J. Good, Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio, The Fibonacci Quarterly 31.1 (1993):7-20. FORMULA a(n) = A331692(n)*a(n-1) + a(n-2) for n >= 2. - Jianing Song, Aug 18 2022 EXAMPLE 1, 4/3, 5/4, 14/11, 159/125, 491/386, 2614/2055, 3105/2441, ... = A225204/A225205 MATHEMATICA Numerator[Convergents[Sqrt[GoldenRatio], 20]] CROSSREFS Cf. A001622, A139339, A331692, A225205 (denominators). Sequence in context: A042535 A222489 A222501 * A363817 A308095 A321348 Adjacent sequences: A225201 A225202 A225203 * A225205 A225206 A225207 KEYWORD nonn,frac AUTHOR Eric W. Weisstein, May 01 2013 STATUS approved

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Last modified July 16 05:19 EDT 2024. Contains 374343 sequences. (Running on oeis4.)