Some Conditions on Periodicity for Sum-Free Sets

Cameron has introduced a natural bijection between the set of one way in nite binary sequences and the set of sum-free sets (of positive integers), and observed that a sum-free set is ultimately periodic only if the corresponding binary sequence is ultimately periodic. He asked if the converse also holds. In this paper we present necessary and sufficient conditions for a sum-free set to be ultimately periodic, and show how these conditions can be used to test specific sets; these tests produce the first evidence of a positive nature that certain sets are, in fact, not ultimately periodic