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- Title
THE MINIMAL GROWTH OF A $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}k$-REGULAR ...
- Authors
BELL, JASON P.; COONS, MICHAEL; HARE, KEVIN G.
- 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 $<INNOPIPE>f(n)<INNOPIPE>>c\log n$ infinitely often. We end our paper by answering a question of Borwein, Choi and Coons on the sums of completely multiplicative automatic functions.
- Subjects
ARITHMETIC functions; MATHEMATICAL functions; NUMBER theory; INTEGERS; ODD numbers
- Publication
Bulletin of the Australian Mathematical Society, 2014, Vol 90, Issue 2, p195
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972714000197