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Archiv der Mathematik

, Volume 79, Issue 1, pp 34–38 | Cite as

Sur la suite des nombres de la forme qn1 + ··· + qnk

  • Y. Bugeaud
Article

Abstract.

Let \( r \geqq 1 \) be an integer and denote by \( \zeta_r \) the root of the polynomial \( X^{r+1} - X^{r} - \cdots - 1 \) belonging to ]1, 2[. Let \( (y_{n }(\zeta_{r}))_n \) be the strictly increasing sequence composed by the real numbers of the form \( \zeta_{r}^{n_1} + \cdots + \zeta_{r}^{n_k} \), the ni‚s being distinct non-negative integers. For \( n \geqq 0 \), set \( u_{n}(\zeta_r) = y_{n+1}(\zeta_r) - y_{n}(\zeta_r) \). The purpose of this note is to give a very precise description of the sequence \( (u_{n}(\zeta_r))_n \), and to show that this is the fixed point of a substitution.

Keywords

Real Number Precise Description 

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • Y. Bugeaud
    • 1
  1. 1.Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg, France,¶ e-mail: bugeaud@math.u-strasbg.frFrance

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