-automatic sequences — such as having an unbordered factor of length
— are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either
-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give a new characterization of the class of
-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems.
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