1 results
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 SEQUENCE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 90 / Issue 2 / October 2014
- Published online by Cambridge University Press:
- 22 May 2014, pp. 195-203
- Print publication:
- October 2014
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- Article
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- You have access
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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.
