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Frobenius Numbers and Automatic Sequences
- Publication Year :
- 2021
-
Abstract
- The Frobenius number $g(S)$ of a set $S$ of non-negative integers with $\gcd 1$ is the largest integer not expressible as a linear combination of elements of $S$. Given a sequence ${\bf s} = (s_i)_{i \geq 0}$, we can define the associated sequence $G_{\bf s} (i) = g(\{ s_i,s_{i+1},\ldots \})$. In this paper we compute $G_{\bf s} (i)$ for some classical automatic sequences: the evil numbers, the odious numbers, and the lower and upper Wythoff sequences. In contrast with the usual methods, our proofs are based largely on automata theory and logic.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2103.10904
- Document Type :
- Working Paper