A225205 Denominators of convergents to the square root of the golden ratio.

1, 3, 4, 11, 125, 386, 2055, 2441, 26465, 28906, 84277, 450291, 1435150, 7626041, 9061191, 25748423, 112054883, 137803306, 249858189, 637519684, 2799936925, 143434302859, 146234239784, 728371261995, 1602976763774, 3934324789543, 123567045239607

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, 33664/26465, ... = A225204/A225205

Mathematica

Denominator[Convergents[Sqrt[GoldenRatio], 20]]

Crossrefs

Cf. A001622, A139339, A331692, A225204 (numerators).

Sequence in context: A102013 A192223 A079940 * A343931 A041299 A001112

Adjacent sequences: A225202 A225203 A225204 * A225206 A225207 A225208

Keyword

nonn,frac

Author

Eric W. Weisstein, May 01 2013

Status

approved