Rarefied Thue-Morse sums via automata theory and logic

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 sigma 0 <= i1)t(3i), using tools from automata theory and logic. The same technique can be used to prove results about analogous sums.(c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).