1. Let $[x]$ denote the greatest integer not exceeding the real number $x$. Set
$$
\begin{array}{l}
A=\{y \mid y=[x]+[2 x]+[4 x], x \in \mathbf{R}\}, \\
B=\{1,2, \cdots, 2019\} .
\end{array}
$$

Then the number of elements in $A \cap B$ is $\qquad$
$-, 1.1154$.
Let $y=f(x)=[x]+[2 x]+[4 x]$. Then $f(x+1)=f(x)+7$.
When $x \in[0,1)$, all possible values of $f(x)$ are $0,1,3,4$.
Therefore, $A=\{7 k, 7 k+1,7 k+3,7 k+4\}(k \in \mathbf{Z})$.
Since $2016=7 \times 288$,
$$
\begin{array}{l}
2017=7 \times 288+1, \\
2019=7 \times 288+3,
\end{array}
$$

Thus, $A \cap B$ has a total of $4 \times 288+2=1154$ elements.