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.
Publié le : 2002-07-05
Classification:
somme des chiffres,
theoreme central limite,
11A67, 11K16,
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
@article{hal-00019871,
author = {Drmota, Michael and Steiner, Wolfgang},
title = {The Zeckendorf expansion of polynomial sequences},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00019871}
}
Drmota, Michael; Steiner, Wolfgang. The Zeckendorf expansion of polynomial sequences. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00019871/