Toeplitz sequences, paperfolding, towers of Hanoi and progression-free sequences of integers (Q1803626)

What is the relationship between folding a piece of paper, moving disks in the classical tower of Hanoi algorithm, and searching for maximal sequences of integers having no \(p\) terms in arithmetic progression? Well might one ask. The authors do, and answer their question by showing that the notion of Toeplitz sequence -- to wit an aperiodic sequence obtained by sequentially filling the `holes' in a periodic sequence by a periodic sequence, as introduced in \textit{K. Jacobs} and \textit{M. Keane} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 13, 123-131 (1969; Zbl 0195.527)], allows a unified description of these matters. The authors' interesting remarks and the extensive list of references makes this a paper well worth study.