The minimal growth of a $k$-regular sequence

J. P. Bell; M. Coons; K. G. Hare

The minimal growth of a $k$ -regular sequence

Authors

J. P. Bell University of Waterloo
M. Coons University of Newcastle
K. G. Hare University of Waterloo

Keywords:

Automata sequences, regular sequences, growth of arithmetic function

Abstract

We determine a lower gap property for the growth of an unbounded

$\mathbb{Z}$ -valued

$k$ -regular sequence. In particular, if

$f:\mathbb{N}\to\mathbb{Z}$ is an unbounded

$k$ -regular sequence, we show that there is a constant

$c>0$ such that

$|f(n)|>c\log n$ infinitely often. We end our paper by answering a question of Borwein, Choi, and Coons on the sums of completely multiplicative automatic functions. DOI: 10.1017/S0004972714000197

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles

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The minimal growth of a kk-regular sequence