• Corpus ID: 51774496

Benford Behavior of Zeckendorf Decompositions

@article{Best2014BenfordBO,
  title={Benford Behavior of Zeckendorf Decompositions},
  author={Andr{\'e} Best and Patrick J. Dynes and Xixi Edelsbrunner and Brian McDonald and Steven J. Miller and Kimsy Tor and Caroline L. Turnage-Butterbaugh and Madeleine Weinstein},
  journal={arXiv: Number Theory},
  year={2014}
}
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers $\{ F_i \}_{i = 1}^{\infty}$. A set $S \subset \mathbb{Z}$ is said to satisfy Benford's law if the density of the elements in $S$ with leading digit $d$ is $\log_{10}{(1+\frac{1}{d})}$; in other words, smaller leading digits are more likely to occur. We prove that, as $n\to\infty$, for a randomly selected integer $m$ in $[0, F_{n+1})$ the distribution of the… 

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