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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
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.
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
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.)