Maximal Sum-Free Set

A maximal sum-free set is a set $\{a_1, a_2, \ldots, a_n\}$ of distinct Natural Numbers such that a maximum $l$ of them satisfy $a_{i_j}+a_{i_k}\not= a_m,$ for $1\leq j<k\leq l$, $1\leq m\leq n$.

See also Maximal Zero-Sum-Free Set

References

Guy, R. K. ``Maximal Sum-Free Sets.'' §C14 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 128-129, 1994.