Rarefied Thue-Morse sums via automata theory and logic

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 ∑0≤i<n(−1)t(3i), using tools from automata theory and logic. The same technique can be used to prove results about analogous sums.