The paper introduces continued fractions based on infinite binary words, suggesting new properties of their expansions.
For each integer n > 1, we present an element in Q((T⁻1)), having a power series expansion based on an infinite word W(n), over the alphabet ${+1;-1}g and whose continued fraction expansion has a particular pattern which is explicitly described. The word W(1) is the Thue-Morse sequence and the following words are defined in a similar way.
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Allombert et al. (2025) studied this question.
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