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 $j - i = k$.

Source of Name

This entry was named for Thoralf Albert Skolem.