Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Aug 18 2022 14:22:33
%S 1,3,4,11,125,386,2055,2441,26465,28906,84277,450291,1435150,7626041,
%T 9061191,25748423,112054883,137803306,249858189,637519684,2799936925,
%U 143434302859,146234239784,728371261995,1602976763774,3934324789543,123567045239607
%N Denominators of convergents to the square root of the golden ratio.
%H 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 I. J. Good, <a href="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 a(n) = A331692(n)*a(n-1) + a(n-2) for n >= 2. - _Jianing Song_, Aug 18 2022
%e 1, 4/3, 5/4, 14/11, 159/125, 491/386, 2614/2055, 3105/2441, 33664/26465, ... = A225204/A225205
%t Denominator[Convergents[Sqrt[GoldenRatio], 20]]
%Y Cf. A001622, A139339, A331692, A225204 (numerators).
%K nonn,frac
%O 0,2
%A _Eric W. Weisstein_, May 01 2013