The Curling Number Conjecture
Abstract
Given a finite nonempty sequence of integers S, by grouping adjacent terms it is always possible to write it, possibly in many ways, as S = X Y^k, where X and Y are sequences and Y is nonempty. Choose the version which maximizes the value of k: this k is the curling number of S. The Curling Number Conjecture is that if one starts with any initial sequence S, and extends it by repeatedly appending the curling number of the current sequence, the sequence will eventually reach 1. The conjecture remains open, but we will report on some numerical results and conjectures in the case when S consists of only 2's and 3's.
Cite
@article{arxiv.0912.2382,
title = {The Curling Number Conjecture},
author = {Benjamin Chaffin and N. J. A. Sloane},
journal= {arXiv preprint arXiv:0912.2382},
year = {2013}
}
Comments
4 pages. Dec 17 2009 fixed a typo. Feb 18 2010: added Ben Chaffin as coauthor, many new results. Sep 24 2012: There was an incorrect lemma in previous version. Paper revised. New version has 8 pages, 6 tables, 1 figure. Feb 17 2013: added comment that there is a sequel to this paper in arXiv:1212.6102