Synchronizing automatic sequences along Piatetski-Shapiro sequences
Abstract
The purpose of this paper is to study subsequences of synchronizing k-automatic sequences a(n) along Piatetski-Shapiro sequences nc with non-integer c>1. In particular, we show that a( nc ) satisfies a prime number theorem of the form Σn x (n)a( nc ) C\, x, and, furthermore, that it is deterministic for c ∈ R Z. As an interesting additional result, we show that the sequence nc m has polynomial subword complexity.
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