Free Fibonacci Sequences
Number Theory
2014-03-20 v1 Combinatorics
Abstract
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze these sequences for small n: 2, 3, 4, and 5. Surprisingly these behaviors are very different. We also talk about any n. Many statements about these sequences are difficult or impossible to prove, but they can be supported by probabilistic arguments, we have plenty of those in this paper. We also introduce ten new sequences. Most of the new sequences are also related to Fibonacci numbers proper, not just free Fibonacci numbers.
Cite
@article{arxiv.1403.4614,
title = {Free Fibonacci Sequences},
author = {Brandon Avila and Tanya Khovanova},
journal= {arXiv preprint arXiv:1403.4614},
year = {2014}
}
Comments
18 pages