Allouche, Jean-Paul; Lubiw, Anna; Mendès France, Michel; van der Poorten, Alfred J.; Shallit, Jeffrey Convergents of folded continued fractions. (English) Zbl 0848.11004 Acta Arith. 77, No. 1, 77-97 (1996). 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 \(\{0, 1, -1\}\). Reviewer: Jeffrey Shallit (Waterloo) Cited in 1 ReviewCited in 4 Documents MSC: 11A55 Continued fractions 11J70 Continued fractions and generalizations 11B85 Automata sequences Keywords:paperfolding; automatic sequence; convergents; continued fractions; formal Laurent series PDFBibTeX XML Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Stern’s diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2*n) = a(n), a(2*n+1) = a(n) + a(n+1). a(4n) = 0, a(4n+2) = 1, a(2n+1) = a(n).