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 \(\{0, 1, -1\}\).


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