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 $i\in\mathb

[学科分类] 离散数学和组合数学

[关键词] Infinite Fibonacci sequence;Singular words;Fibonacci number;Digit sum