Some Properties of the Fibonacci Sequence on an Infinite Alphabet

摘要

The infinite Fibonacci sequence $mathbf{F}$, which is an extension of the classic Fibonacci sequence to the infinite alphabet $mathbb{N}$, is the fixed point of the morphism $phi$: $(2i)mapsto (2i)(2i+1)$ and $(2i+1)mapsto (2i+2)$ for all $iinmathbb{N}$. In this paper, we study the growth order and digit sum of $mathbf{F}$?and give several decompositions of $mathbf{F}$ using singular words. Author Biographies Jiemeng Zhang, Wuhan Institute of Technology PhD in Math.