Stanley sequence

In mathematics, a Stanley sequence is an integer sequence generated by a greedy algorithm that chooses the sequence members to avoid arithmetic progressions. If ${\displaystyle S}$ is a finite set of non-negative integers on which no three elements form an arithmetic progression (that is, a Salem–Spencer set), then the Stanley sequence generated from ${\displaystyle S}$ starts from the elements of ${\displaystyle S}$, in sorted order, and then repeatedly chooses each successive element of the sequence to be a number that is larger than the already-chosen numbers and does not form any three-term arithmetic progression with them. These sequences are named after Richard P. Stanley.