Cameron has introduced a natural one-to-one correspondence between
infinite binary sequences and sets of positive integers with
the property that no two elements add up to a third. He observed
that, if a sum-free set is ultimately periodic, so is the
corresponding binary sequence, and asked if the converse also holds.
We present here 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.