# Benford Behavior of Generalized Zeckendorf Decompositions

@article{Best2015BenfordBO,
title={Benford Behavior of Generalized Zeckendorf Decompositions},
author={Andrew 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={2015},
pages={25-37}
}
• Andrew Best, +5 authors Madeleine Weinstein
• Published 2015
• Mathematics
• arXiv: Number Theory
• We prove connections between Zeckendorf decompositions and Benford’s law. Recall that if we define the Fibonacci numbers by $$F_1 = 1, F_2 = 2$$, and $$F_{n+1} = F_n + F_{n-1}$$, every positive integer can be written uniquely as a sum of nonadjacent elements of this sequence; this is called the Zeckendorf decomposition, and similar unique decompositions exist for sequences arising from recurrence relations of the form $$G_{n+1}=c_1G_n+\cdots +c_LG_{n+1-L}$$ with $$c_i$$ positive and some other… CONTINUE READING

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