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ON MINIMAL ASYMPTOTIC
$g$-ADIC BASES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 05 August 2015, pp. 374-379
- Print publication:
- December 2015
-
- Article
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- You have access
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Let
$g\geq 2$ be a fixed integer. Let 
$\mathbb{N}$ denote the set of all nonnegative integers and let 
$A$ be a subset of 
$\mathbb{N}$. Write 
$r_{2}(A,n)=\sharp \{(a_{1},a_{2})\in A^{2}:a_{1}+a_{2}=n\}.$ We construct a thin, strongly minimal, asymptotic 
$g$-adic basis 
$A$ of order two such that the set of 
$n$ with 
$r_{2}(A,n)=2$ has density one.
