2001 OIM Problems/Problem 4

Problem

Find the maximum number of increasing arithmetic progressions of three terms that can have a sequence $a_1 < a_2 < \cdots < a_n$ of $n \ge 3$ real numbers.

Note: Three terms $a_i, a_j , a_k$ of a sequence of real numbers form an increasing arithmetic progression if $a_i < a_j < a_k$ and $a_j - a_i = a_k - a_j$ .

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2001 OIM Problems/Problem 4

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