16. Let the sequence $\left\{ a _ { n } \right\}$ have the sum of the first $n$ terms $S _ { n } = 2 a _ { n } - a _ { 3 }$, and $a _ { 1 }$, $a _ { 2 } + 1$, $a _ { 3 }$ form an arithmetic sequence.\\
(1) Find the general term formula of the sequence $\left\{ a _ { n } \right\}$;\\
(2) Let $T _ { n }$ be the sum of the first $n$ terms of the sequence $\left\{ \frac { 1 } { a _ { n } } \right\}$. Find the minimum value of $n$ such that $\left| T _ { n } - 1 \right| < \frac { 1 } { 1000 }$.