Sum-free sets generated by the period-k-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.