Seven, given a sequence whose terms are 1 or 2, the first term is 1, and there are $2^{k-1}$ 2s between the $k$-th 1 and the $(k+1)$-th 1, i.e., $1,2,1,2,2,1,2,2,2,2,1,2,2,2,2,2,2,2,2,1, \cdots$
(1) Find the sum of the first 1998 terms of the sequence $S_{1998}$;
(2) Does there exist a positive integer $n$ such that the sum of the first $n$ terms of the sequence $S_{n}=2001$? If $n$ exists, find the value of $n$; if $n$ does not exist, prove your conclusion.