Combinatorics and Graph Theory

   

Even FibBinary Numbers and the Golden Ratio

Authors: J Gregory Moxness

Previously, a determination of the relationship between the Natural numbers (N) and the n'th odd fibbinary number has been made using a relationship with the Golden ratio \phi=(Sqrt[5]+1}/2 and \tau=1/\phi. Specifically, if the n'th odd fibbinary equates to the j'th N, then j=Floor[n(\phi+1) - 1]. This note documents the completion of the relationship for the even fibbinary numbers, such that if the n'th even fibbinary equates to the j'th N, then j=Floor[n(\tau+1) + \tau].

Comments: 4 Pages.

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Submission history

[v1] 2018-12-30 19:20:53

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