1. Arrange positive integers starting from 1 in a number array according to the pattern shown in Figure 2, where 2 is at the 1st corner, 3 is at the 2nd corner, 5 is at the 3rd corner, 7 is at the 4th corner, $\cdots \cdots$. Then, the number at the 2007th corner is $\qquad$

Figure 2
$$
\begin{array}{l}
a_{1}=2, a_{2 i}=a_{2 i-1}+i, \\
a_{2 i+1}=a_{2 i}+(i+1) .
\end{array}
$$

Since $2007=2 \times 1003+1$, we have,
$$
\begin{array}{l}
a_{2007}=1+2(1+2+\cdots+1003)+1004 \\
=1004^{2}+1=1008017 .
\end{array}
$$