Consider the sequence of numbers defined recursively by $t_1=1$ and for $n>1$ by $t_n=1+t_{n/2}$ when $n$ is even and by $t_n=\frac{1}{t_{n-1}}$ when $n$ is odd. Given that $t_n=\frac{19}{87}$, find $n.$

What I did: I tried to work backwards from $t_n=19/87$ to $t_1=1$

but it's not working out -_-

Guest May 25, 2021