%I #38 Aug 05 2017 19:46:38
%S 1,1,2,2,1,6,2,2,6,5,4,4,1,10,8,4,3,2,8,14,2,12,10,4,11,5,14,10,4,28,
%T 8,8,8,1,20,2,7,4,8,14,6,6,18,8,24,6,2,4,22,31,12,14,9,10,2,12,16,12,
%U 20,20,5,8,8,20,13,20,22,2,10,52,28,2,15,19,36,4
%N Length of the period of the continued fraction expansion of phi/n where phi is the golden ratio.
%C We calculated the continued fraction expansion of phi/n and observed that the expansion is periodic after the first nonzero term. We tracked the periodicity of the expansions and present them here. The authors acknowledge the National Science Foundation (DMS-1560019) and Muhlenberg College for supporting the REU (Research Experiences for Undergraduates) on which this sequence is based.
%H Alois P. Heinz, <a href="/A290013/b290013.txt">Table of n, a(n) for n = 1..10000</a>
%t a[n_] := ContinuedFraction[GoldenRatio/n] // Last // Length; Array[a, 80] (* _Jean-François Alcover_, Jul 28 2017 *)
%Y Cf. A001622 (phi), A019863 (phi/2), A134943 (phi/3), A134944 (phi/4), A134946 (phi/6).
%K nonn,look,easy
%O 1,3
%A _Vanessa Gomez_, _Eric Jovinelly_, _Jacob A. McCann_, _Bryce Orloski_, _Catherine Rea_, _Shannon Talbott_, Jul 17 2017