An explicit formula generating the non-Fibonacci numbers

Details An explicit formula generating the non-Fibonacci numbers An explicit formula generating the non-Fibonacci numbers

2011-05-05

arxiv.org/abs/1105.1127v2

Mathematics

Number Theory

5 pages

Scientific paper

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

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