Definition:Skolem Sequence

A Skolem sequence of order $$n$$ is a sequence $$S=\{s_1,s_2,...,s_{2n}\}$$ of $$2n$$ integers for which 1. For every $$k \in \{1,2,...,n\}$$ 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 $$j-i=k$$