Journal of Integer Sequences, Vol. 26 (2023), Article 23.5.5

Golden Ratio Base Expansions of the Logarithm and Inverse Tangent of Fibonacci and Lucas Numbers


Kunle Adegoke
Department of Physics and Engineering Physics
Obafemi Awolowo University
Ile-Ife
Nigeria

Jaume Oliver Lafont
Conselleria d'Educacio i Cultura
Govern de les Illes Balears
Palma Spain

Abstract:

Let α = (1+√5)/2, the golden ratio. Let Fn and Ln be the Fibonacci and Lucas numbers. We derive base-α expansions of log Fn, log Ln, arctan 1/Fn, and arctan 1/Ln for all positive integers n.

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(Concerned with sequences A000032 A000045.)

Received March 19 2023; revised version received March 30 2023. Published in Journal of Integer Sequences, June 6 2023.

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