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 A290013 Length of the period of the continued fraction expansion of phi/n where phi is the golden ratio. 1
 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, 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, 20, 20, 5, 8, 8, 20, 13, 20, 22, 2, 10, 52, 28, 2, 15, 19, 36, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 MATHEMATICA a[n_] := ContinuedFraction[GoldenRatio/n] // Last // Length; Array[a, 80] (* Jean-François Alcover, Jul 28 2017 *) CROSSREFS Cf. A001622 (phi), A019863 (phi/2), A134943 (phi/3), A134944 (phi/4), A134946 (phi/6). Sequence in context: A326617 A326962 A280245 * A220963 A179313 A209692 Adjacent sequences:  A290010 A290011 A290012 * A290014 A290015 A290016 KEYWORD nonn,look,easy AUTHOR Vanessa Gomez, Eric Jovinelly, Jacob A. McCann, Bryce Orloski, Catherine Rea, Shannon Talbott, Jul 17 2017 STATUS approved

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Last modified February 27 12:47 EST 2020. Contains 332306 sequences. (Running on oeis4.)