Algebraic automatic continued fractions in characteristic $2$ II
Abstract
We present two families of automatic sequences that define algebraic continued fractions in characteristic $2$. The period-doubling sequence belongs to the first first family $\mathcal{P}$; and its sum, the Thue-Morse sequence, belongs to the second family $\mathcal{G}$. The family $\mathcal{G}$ contains all the iterated sums of sequences from the $\mathcal{P}$ and more.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- arXiv:
- arXiv:2301.09958
- Bibcode:
- 2023arXiv230109958H
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Combinatorics;
- 11B85;
- 11J70;
- 11B50;
- 11Y65;
- 05A15;
- 11T55