The Zeckendorf expansion of polynomial sequences

Michael Drmota (1) , Wolfgang Steiner (1)

1 Institut für Geometrie

In the first part of the paper we prove that the Zeckendorf sum-of-digits function $s_Z(n)$ and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the $q$-ary expansions of integers are asymptotically independent.

Mots clés: somme des chiffres; theoreme central limite

Domaines: Théorie des nombres [math.NT]

Michael Drmota, Wolfgang Steiner. The Zeckendorf expansion of polynomial sequences. Journal de Théorie des Nombres de Bordeaux, 2002, 14, pp.439-475. ⟨hal-00019871⟩