Stanley sequence

Mathematical sequence involving arithmetic progressions

In mathematics, a Stanley sequence is an integer sequence generated by a greedy algorithm that chooses the sequence members to avoid arithmetic progressions. If is a finite set of non-negative integers on which no three elements form an arithmetic progression, then the Stanley sequence generated from starts from the elements of , 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.

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