4 citations · 8 across the 15 of their papers we have counts for
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On the Enumeration and Asymptotic Analysis of Fibonacci Compositions
Joshua M. Siktar
We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the num…
Walking to Infinity Along Some Number Theory sequences
Steven J. Miller, Fei Peng, Tudor Popescu +3
An interesting open conjecture asks whether it is possible to walk to infinity along primes, where each term in the sequence has one digit more than the previous. We present differ…
Zeckendorf's Theorem Using Indices in an Arithmetic Progression
Amelia Gilson, Hadley Killen, Tamás Lengyel +4
Zeckendorf's Theorem states that any positive integer can be uniquely decomposed into a sum of distinct, non-adjacent Fibonacci numbers. There are many generalizations, including r…
Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice
Evan Fang, Jonathan Jenkins, Zack Lee +5
Zeckendorf proved that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , and later researchers showed that the distribution of the numb…
Gaussian Behavior in Zeckendorf Decompositions From Lattices
Eric Chen, Robin Chen, Lucy Guo +4
Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. We consider higher-dimensional lattice analogues, where a…