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 $$j - i = k$$.