The Fibonacci Sequence is Normal Base 10
Number Theory
2022-02-21 v1
Abstract
In this paper, we show that the concatenation of the Fibonacci sequence is \textit{normal} in base , meaning every string of a given length, , occurs as frequently as every other string of length (there are as many 's as 's and as many 's and 's). Although we know that almost every number is normal, we can name very few of them. It is still unclear if , , or are normal. We show that concatenating the Fibonacci sequence behind a decimal creates a normal number in every base of the form . We then provide evidence that potentially extends our result to all integer bases, and claim that the Fibonacci concatenation is \textit{absolutely normal}.
Cite
@article{arxiv.2202.08986,
title = {The Fibonacci Sequence is Normal Base 10},
author = {Brennan Benfield and Michelle Manes},
journal= {arXiv preprint arXiv:2202.08986},
year = {2022}
}