Gap spectra and densities of slow Fibonacci walks

Yaping Mao, Qinghong Zhao

Let $F_1=F_2=1$ and $F_{t+2}=F_{t+1}+F_t$ for $t\ge 1$. For every $n\ge 2$, there are unique integers $a,b,t$ such that $n=a{F}_t+b{F}_{t-1}$ with $t\ge 2$ and $1\le a\le b\le F_t$.…