16.2.16 * Find the smallest natural number $n$ that satisfies the following properties: (1) $n$ ends with 6 in its decimal representation; (2) when the last digit 6 of $n$ is moved to the front, the resulting number is four times $n$.
Let $n=10 m+6$, then $6 \times 10^{k}+m=4(10 m+6)$, where $k$ is the number of digits in $m$. Thus, $m=\frac{2}{13}\left(10^{k}-4\right)$, to make $m$ an integer, $k$ must be at least 5. When $k=5$, $n=153846$.