1Laboratoire de Mathematiques appliquees, Faculte des Sciences Exactes, Universite de Bejaia, Bejaia, Algeria
Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 2, pp. 291-299
Citer cet article
Bakir Farhi; Bakir Farhi. On the possible quantities of Fibonacci numbers that occur in some type of intervals. Acta mathematica Universitatis Comenianae, Tome 87 (2018) no. 2, pp. 291-299. http://geodesic.mathdoc.fr/item/AMUC_2018_87_2_a11/
@article{AMUC_2018_87_2_a11,
author = {Bakir Farhi and Bakir Farhi},
title = { On the possible quantities of {Fibonacci} numbers that occur in some type of intervals},
journal = {Acta mathematica Universitatis Comenianae},
pages = {291--299},
year = {2018},
volume = {87},
number = {2},
url = {http://geodesic.mathdoc.fr/item/AMUC_2018_87_2_a11/}
}
TY - JOUR
AU - Bakir Farhi
AU - Bakir Farhi
TI - On the possible quantities of Fibonacci numbers that occur in some type of intervals
JO - Acta mathematica Universitatis Comenianae
PY - 2018
SP - 291
EP - 299
VL - 87
IS - 2
UR - http://geodesic.mathdoc.fr/item/AMUC_2018_87_2_a11/
ID - AMUC_2018_87_2_a11
ER -
%0 Journal Article
%A Bakir Farhi
%A Bakir Farhi
%T On the possible quantities of Fibonacci numbers that occur in some type of intervals
%J Acta mathematica Universitatis Comenianae
%D 2018
%P 291-299
%V 87
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2018_87_2_a11/
%F AMUC_2018_87_2_a11
In this paper, we show that for any integer a \geq 2, each of the intervals[a^k; a^{k+1}) (k \in N) contains either ⌊\log a/\log\Phi ⌋ or ⌈\log a/\log\Phi⌉ Fibonacci numbers. In addi-tion, the density (in N) of the set of the all natural numbers k for which the interval[a^k; a^{k+1}) contains exactly ⌊\log a/\log\Phi ⌋ Fibonacci numbers is equal to (1 - \langle\log a/\log\Phi\rangle) and the density of the set of the all natural numbers k for which the interval[a^k; a^{k+1}) contains exactly ⌈\log a/\log\Phi⌉ Fibonacci numbers is equal to \langle\log a/\log\Phi\rangle.
