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arXiv · 1207.5450

Least periods of k-automatic sequences

Daniel Goc·Jeffrey Shallit
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Abstract

Currie and Saari initiated the study of least periods of infinite words, and they showed that every integer n >= 1 is a least period of the Thue-Morse sequence. We generalize this result to show that the characteristic sequence of least periods of a k-automatic sequence is (effectively) k-automatic. Through an implementation of our construction, we confirm the result of Currie and Saari, and we obtain similar results for the period-doubling sequence, the Rudin-Shapiro sequence, and the paperfolding sequence.

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Daniel Goc, Jeffrey Shallit. 2012-07-23. Least periods of k-automatic sequences. https://arxiv.org/abs/1207.5450

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