1. Given the sequence $\left\{a_{n}\right\}$ satisfies:
$$
a_{1}=1, a_{n}=5 a_{n-1}+3^{n-1}(n \geqslant 2) \text {. }
$$

Find $a_{n}$ and the highest power of 2 that divides $a_{k}\left(k=2^{2019}\right)$