When is an automatic set an additive basis?
Jason P. Bell, Kathryn E. Hare, Jeffrey O. Shallit · Proceedings of the American Mathematical Society Series B · 2018
We characterize those k k -automatic sets S 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 j such that S S forms an additive basis of order j j , if it exists.