Sum-free sets generated by the period-[formula omitted]-folding sequences and some Sturmian sequences

Abstract

First, we show that the sum-free set generated by the period-doubling sequence is not κ-regular for any κ≥2. Next, we introduce a generalization of the period-doubling sequence, which we call the period-k-folding sequences. We show that the sum-free sets generated by the period-k-folding sequences also fail to be κ-regular for all κ≥2. Finally, we study the sum-free sets generated by Sturmian sequences that begin with ‘11’, and their difference sequences.