MathNet 2017-part-02 — 176 problems (EN–VI) Question 4

A number written only with digits $2$ and $3$ is called *happy*. Therefore, the happy numbers are $2$, $3$, $22$, $23$, $32$, $33$, $222$, $223$, $232$, $233$, $322$, $323$, $332$, $333$, ... Determine the $2050$th happy number.