Skolem Sequence

A Skolem sequence of order $n$ is a sequence $S=\{s_1, s_2, \ldots, s_{2n}\}$ of $2n$ integers such that

1. For every $k\in\{1, 2, \ldots, n\}$, there exist exactly two elements $s_i, s_j\in S$ such that $s_i=s_j=k$, and

2. If $s_i=s_j=k$ with $i<j$, then $j-i=k$.

References

Colbourn, C. J. and Dinitz, J. H. (Eds.) ``Skolem Sequences.'' Ch. 43 in CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, pp. 457-461, 1996.