11. The sequence $\left\{a_{n}\right\}$ is: $1,1,2,1,1,2,3,1,1,2,1,1,2,3,4, \cdots$, that is, first take $a_{1}=1$, then copy this item and paste it behind as $a_{2}$, and add the successor number 2 as $a_{3}$, then copy all items $1,1,2$ and paste them behind as $a_{4}, a_{5}, a_{6}$, and add the successor number 3 as $a_{7}, \cdots$ and continue in this manner. Then $a_{2021}=$ $\qquad$
The sequence $\left\{a_{n}\right\}$ is grouped as: $1 ; 1,2 ; 1,1,2,3 ; 1,1,2,1,1,2,3,4 ; 1,1,2,1,1,2,3,1,1,2,1,1$,
$2,3,4,5 ; \cdots$, from which we can see that $a_{1}=1, a_{3}=2, a_{7}=3, a_{15}=4, a_{31}=5$, and $a_{2^{n}-1+k}=a_{k}$.
Therefore, $a_{2021}=a_{2^{10}-1+998}=a_{998}=a_{2^{9}-1+487}=a_{487}=a_{2^{8}-1+232}=a_{232}=a_{2^{7}-1+105}$
$=a_{105}=a_{2^{6}-1+42}=a_{42}=a_{2^{5}-1+11}=a_{11}=a_{2^{3}-1+4}=a_{4}=a_{2^{2}-1+1}=a_{1}=1$.