The Zeckendorf expansion of polynomial sequences
Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 2, p. 439-475

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.

Nous montrons que la fonction æsomme de chiffresÆ de Zeckendorf s z (n) lorsque n parcourt l’ensemble des nombres premiers ou bien une suite polynomiale d’entiers satisfait un théorème central limite. Nous obtenons aussi des résultats analogues pour d’autres fonctions du même type. Nous montrons également que le développement de Zeckendorf et le développement standard en base q des entiers sont asymptotiquement indépendants.

@article{JTNB_2002__14_2_439_0,
     author = {Drmota, Michael and Steiner, Wolfgang},
     title = {The Zeckendorf expansion of polynomial sequences},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     pages = {439-475},
     zbl = {1077.11005},
     mrnumber = {2040687},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2002__14_2_439_0}
}
Drmota, Michael; Steiner, Wolfgang. The Zeckendorf expansion of polynomial sequences. Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 2, pp. 439-475. http://www.numdam.org/item/JTNB_2002__14_2_439_0/

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