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arXiv · 1710.08353

When is an automatic set an additive basis?

Jason Bell·Kathryn Hare·Jeffrey Shallit
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Abstract

We characterize those $k$-automatic sets $S$ of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest $j$ such that $S$ forms an additive basis of order $j$, if it exists.

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Jason Bell, Kathryn Hare, Jeffrey Shallit. 2017-10-23. When is an automatic set an additive basis?. https://arxiv.org/abs/1710.08353

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