cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A225205 #16 Jan 05 2025 19:51:40
%S A225205 1,3,4,11,125,386,2055,2441,26465,28906,84277,450291,1435150,7626041,
%T A225205 9061191,25748423,112054883,137803306,249858189,637519684,2799936925,
%U A225205 143434302859,146234239784,728371261995,1602976763774,3934324789543,123567045239607
%N A225205 Denominators of convergents to the square root of the golden ratio.
%H A225205 I. J. Good, <a href="https://doi.org/10.1057/jors.1992.123">Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio (Condensed Version)</a>, Journal of the Operational Research Society, 43 (1992), 837-842.
%H A225205 I. J. Good, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/31-1/good.pdf">Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio</a>, The Fibonacci Quarterly 31.1 (1993):7-20.
%F A225205 a(n) = A331692(n)*a(n-1) + a(n-2) for n >= 2. - _Jianing Song_, Aug 18 2022
%e A225205 1, 4/3, 5/4, 14/11, 159/125, 491/386, 2614/2055, 3105/2441, 33664/26465, ... = A225204/A225205
%t A225205 Denominator[Convergents[Sqrt[GoldenRatio], 20]]
%Y A225205 Cf. A001622, A139339, A331692, A225204 (numerators).
%K A225205 nonn,frac
%O A225205 0,2
%A A225205 _Eric W. Weisstein_, May 01 2013