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)