# Consecutive Triples Of Numbers

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.

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