When is an automatic set an additive basis?

Published 23 Oct 2017 in math.NT, cs.DM, cs.FL, and math.CO | (1710.08353v1)

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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