Converse to Cameron’s ultimate-periodicity result

Determine whether ultimate periodicity of a greedy non-strict 2-sumfree sequence implies ultimate periodicity of the binary sequence governing its construction.

Background

The paper describes a bijective framework for greedy non-strict 2-sumfree sequences in which a binary sequence determines whether eligible integers are included. Cameron proved that an ultimately periodic binary sequence produces an ultimately periodic sumfree sequence.

The converse implication is explicitly unresolved in the cited discussion; the authors note that computations have found periodic candidates for the binary sequence that appear to generate aperiodic sumfree sequences, but this does not settle the general question.