

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
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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 (DMS1560019) 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] (* JeanFrançois 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



