ON GENERALIZED STANLEY SEQUENCES.

Let N denote the set of all nonnegative integers. Let k≥3 be an integer and A0={a1,...,at}(a1<...<at) be a nonnegative set which does not contain an arithmetic progression of length k. We denote A={a1,a2,...} defined by the following greedy algorithm: if l≥t and a1,...,al have already been defined, then al+1 is the smallest integer a>al such that {a1,...,al}∪{a} also does not contain a k-term arithmetic progression. This sequence A is called the Stanley sequence of order k generated by A0. We prove some results about various generalizations of the Stanley sequence. [ABSTRACT FROM AUTHOR]