Regularity versus complexity in the binary representation of 3^n
Number Theory
2015-03-13 v2
Abstract
We use the grid consisting of bits of 3^n to motivate the definition of 2-adic numbers. Specifically, we exhibit diagonal stripes in the bits of 3^(2^n), which turn out to be the first in an infinite sequence of such structures. Our observations are explained by a 2-adic power series, providing some regularity among the disorder in the bits of powers of 3. Generally, the base-p representation of k^(p^n) has these features.
Cite
@article{arxiv.0902.3257,
title = {Regularity versus complexity in the binary representation of 3^n},
author = {Eric S. Rowland},
journal= {arXiv preprint arXiv:0902.3257},
year = {2015}
}
Comments
10 pages, 7 figures; published version