Benford Behavior of Generalized Zeckendorf Decompositions

  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},
  • Andrew Best, Patrick J. Dynes, +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