On Collatz' Words, Sequences and Trees
Number Theory
2015-02-04 v1
Abstract
Motivated by a recent work of Tr\"umper we consider the general Collatz word (up-down pattern) and the sequences following this pattern. The recurrences for the first and last sequence entries are given, obtained from repeated application of the general solution of a binary linear inhomogeneous Diophantine equation. These recurrences are then solved. The Collatz tree is also discussed.
Keywords
Cite
@article{arxiv.1404.2710,
title = {On Collatz' Words, Sequences and Trees},
author = {Wolfdieter Lang},
journal= {arXiv preprint arXiv:1404.2710},
year = {2015}
}
Comments
13 pages, 1 figure