Question 23
Let $N=\overline{a_1a_2\cdots a_7}$ be a 7-digit whole number formed by the digits from $1$ to $9$ (the digits may repeat). Suppose that for each $k=1,2,3,4,5$, the 3-digit number $\overline{a_ka_{k+1}a_{k+2}}$ formed by three consecutive digits of $N$ is divisible by $3$. How many such numbers $N$ are there?