Rarefied Thue-Morse Sums Via Automata Theory and Logic

Jeffrey Shallit

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arXiv · 2302.09436

Rarefied Thue-Morse Sums Via Automata Theory and Logic

Jeffrey Shallit

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Abstract

Let $t(n)$ denote the number of $1$-bits in the base-$2$ representation of $n$, taken modulo $2$. We show how to prove the classic conjecture of Leo Moser, on the rarefied sum $\sum_{0\leq i<n} (-1)^{t(3i)}$, using tools from automata theory and logic. The same technique can be used to prove results about analogous sums.

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Jeffrey Shallit. 2023-02-18. Rarefied Thue-Morse Sums Via Automata Theory and Logic. https://arxiv.org/abs/2302.09436

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