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arXiv · 1105.1127

An explicit formula generating the non-Fibonacci numbers

Bakir Farhi
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Abstract

We show among others that the formula: $$ \lfloor n + \log_Φ\{\sqrt{5}(\log_Φ(\sqrt{5}n) + n) -5 + \frac{3}{n}\} - 2 \rfloor (n \geq 2), $$ (where $Φ$ denotes the golden ratio and $\lfloor \rfloor$ denotes the integer part) generates the non-Fibonacci numbers.

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Bakir Farhi. 2011-05-10. An explicit formula generating the non-Fibonacci numbers. https://arxiv.org/abs/1105.1127

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