Definition:Skolem Sequence

Definition
A Skolem sequence of order $n$ is a sequence $S = \left\{{s_1, s_2, \ldots, s_{2 n}}\right\}$ of $2 n$ integers for which:
 * $(1): \quad$ 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:
 * $(2): \quad$ If $s_i = s_j = k$ and $i < j$ then $j - i = k$.