Advanced Number Theory · Challenge problem

A positive integer $N$ has exactly three digits $a,b,c$ when written in base $8$ (so $N = 64a+8b+c$ with $1 \le a \le 7$ and $0\le b,c\le7$). When those same three digits, reversed, are read as a base-$9$ numeral, the result equals $2N$. Find $N$.