Call a positive integer $$N$$ a $$\textit{7-10 double}$$ if the digits of the base-7 representation of $$N$$ form a base-10 number that is twice $$N$$. For example, $$51$$ is a 7-10 double because its base-7 representation is $$102$$. What is the largest 7-10 double?

(第十九届AIME1 2001 第8题)