## Convergents of folded continued fractions.(English)Zbl 0848.11004

Let $$\varepsilon_i= \pm 1$$ for $$i\geq 0$$. We discuss the convergents of the continued fractions of two formal Laurent series in $$\mathbb{Q} ((X^{-1}))$$: $$g_\varepsilon (X)= \sum_{i\geq 0} \varepsilon_i X^{-2^i}$$ and $$h_\varepsilon (X)= Xg(X)$$. In particular, we show that the denominators of the convergents to both series have the remarkable property that their coefficients all lie in $$\{0, 1, -1\}$$.

### MSC:

 11A55 Continued fractions 11J70 Continued fractions and generalizations 11B85 Automata sequences
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