A sequence of positive integers with $$a_1=1$$ and $$a_9+a_{10}=646$$ is formed so that the first three terms are in geometric progression, the second, third, and fourth terms are in arithmetic progression, and, in general, for all $$n\ge1,$$ the terms $$a_{2n-1}, a_{2n}, a_{2n+1}$$ are in geometric progression, and the terms $$a_{2n}, a_{2n+1},$$ and $$a_{2n+2}$$ are in arithmetic progression. Let $$a_n$$ be the greatest term in this sequence that is less than 1000. Find $$n+a_n.$$

(第二十二届AIME2 2004 第9题)