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An explicit formula generating the non-Fibonacci numbers
Published 5 May 2011 in math.NT | (1105.1127v2)
Abstract: 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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