A set of positive integers is double-free if, for any integer x, the set {x, 2x}⊈S (or equivalently, x element S implies 2x not element S). For example, of the subsets of {1, 2, 3}, the sets ∅, {1}, {2}, {2, 3}, {1, 3}, and {3} are double-free, while {1, 2} and {1, 2, 3} are not.

A-sequence | binary | Klarner-Rado sequence | sum-free set | triple-free set