# Consecutive Triples Of Numbers

**Discrete Mathematics**Level 5

Let \(\{a_1, a_2, \cdots , a_{2013}\}\) be a set of \(2013\) positive integers. Three distinct integers \(1 \leq i, j, k \leq 2013\) are called *good* if \(a_k - a_j = a_j - a_i = 1.\) Find the last three digits of the maximum possible number of good triples \(\{i, j, k\}\).

**Details and assumptions**

Two good triples \(\{i, j, k\}\) and \(\{m, n, p\}\) are considered distinct if they differ in at least one number.

Yes, it's \(2013,\) not \(2014\).

This problem is not original.

A mistake in the wording has been fixed. Apologies.