login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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