Definition:Skolem Sequence

Definition
A Skolem sequence of order $n$ is a sequence $S = \left\{{s_1, s_2, \ldots, s_{2n}}\right\}$ of $2n$ integers for which:


 * 1) For every $k \in \left\{{1, 2, \ldots, n}\right\}$ there exist exactly two elements $s_i, s_j \in S$ so that $s_i = s_j = k$, and
 * 2) If $s_i = s_j = k$ and $i < j$ then $j - i = k$.