3. Let the sequence $\left\{a_{n}\right\}$ satisfy
$$
a_{1}=\sqrt{3}, a_{n+1}=\left[a_{n}\right]+\frac{1}{\left\{a_{n}\right\}},
$$

where, $\left[a_{n}\right] 、\left\{a_{n}\right\}$ represent the integer part and the fractional part of the positive number $a_{n}$, respectively. Then $a_{2015}=$ $\qquad$
3. $3021+\sqrt{3}$.

From the given, we have
$$
\begin{array}{l}
a_{1}=1+(\sqrt{3}-1), \\
a_{2}=1+\frac{1}{\sqrt{3}-1}=2+\frac{\sqrt{3}-1}{2} .
\end{array}
$$

It is easy to see that $a_{2 k+1}=3 k+1+(\sqrt{3}-1)$,
$$
a_{2 k+2}=3 k+2+\frac{\sqrt{3}-1}{2} \text { . }
$$

Therefore, $a_{2015}=3022+(\sqrt{3}-1)=3021+\sqrt{3}$.