The Fibonacci sequence and Schreier-Zeckendorf sets
HV Chu - arXiv preprint arXiv:1906.10962, 2019 - arxiv.org
A finite subset of the natural numbers is weak-Schreier if $\min S\ge| S| $, strong-Schreier if
$\min S>| S| $, and maximal if $\min S=| S| $. Let $ M_n $ be the number of weak-Schreier …
$\min S>| S| $, and maximal if $\min S=| S| $. Let $ M_n $ be the number of weak-Schreier …
Benford behavior and distribution in residue classes of large prime factors
P Pollack, AS Roy - Canadian Mathematical Bulletin, 2023 - cambridge.org
We investigate the leading digit distribution of the kth largest prime factor of n (for each fixed)
as well as the sum of all prime factors of n. In each case, we find that the leading digits are …
as well as the sum of all prime factors of n. In each case, we find that the leading digits are …
On Zeckendorf related partitions using the Lucas sequence
H Việt Chu, D C. Luo, S J. Miller - The Fibonacci Quarterly, 2022 - Taylor & Francis
Zeckendorf proved that every positive integer has a unique partition as a sum of
nonconsecutive Fibonacci numbers. Similarly, every natural number can be partitioned into …
nonconsecutive Fibonacci numbers. Similarly, every natural number can be partitioned into …
Benford behavior of generalized Zeckendorf decompositions
A Best, P Dynes, X Edelsbrunner, B McDonald… - … and Additive Number …, 2015 - Springer
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if
we define the Fibonacci numbers by F_1= 1, F_2= 2, and F_ n+ 1= F_n+ F_ n-1, every …
we define the Fibonacci numbers by F_1= 1, F_2= 2, and F_ n+ 1= F_n+ F_ n-1, every …
On Generalized Zeckendorf Decompositions and Generalized Golden Strings
HV Chu - The Fibonacci Quarterly, 2021 - Taylor & Francis
Zeckendorf proved that every positive integer has a unique representation as a sum of
nonconsecutive Fibonacci numbers. A natural generalization of this theorem is to look at the …
nonconsecutive Fibonacci numbers. A natural generalization of this theorem is to look at the …
Difference in the Number of Summands in the Zeckendorf Partitions of Consecutive Integers
HV Chu - arXiv preprint arXiv:2010.15592, 2020 - arxiv.org
Zeckendorf proved that every positive integer has a unique partition as a sum of non-
consecutive Fibonacci numbers. We study the difference between the number of summands …
consecutive Fibonacci numbers. We study the difference between the number of summands …