A225204 Numerators of convergents to the square root of the golden ratio.

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

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