1. If a positive integer cannot be expressed as the difference of squares of two positive integers, then this positive integer is called a "non-wise number". If these non-wise numbers are arranged in ascending order, then the 2009th non-wise number is $\qquad$
ニ、1.8026.
1 cannot be expressed as the difference of squares of two positive integers, so 1 is the 1st non-wise number.

Odd numbers greater than 1, $2 n+1\left(n \in N_{+}\right)$, can be expressed as $(n+1)^{2}-n^{2}$.

Even numbers divisible by 4, $4 m$, can be expressed as $(m+1)^{2}-(m-1)^{2}(m>1)$. However, 4 cannot be expressed as the difference of squares of two positive integers. Even numbers divisible by 2 but not by 4, $4 m+2(m \in N)$, cannot be expressed as the difference of squares of two positive integers. Otherwise,
$$
x^{2}-y^{2}=(x+y)(x-y)=4 m+2 \text {. }
$$

Since $x+y$ and $x-y$ have the same parity, and $4 m+2$ is even, therefore, $x+y$ and $x-y$ are both even.
Thus, $2|(x+y), 2|(x-y)$.
Hence, $4 \mid\left(x^{2}-y^{2}\right)$.
Therefore, $4 \mid(4 m+2)$, which contradicts $4 \nmid(4 m+2)$.
So, $4 m+2$ is a non-wise number.
Thus, the non-wise numbers arranged in ascending order are:
$1,2,4,6,10,14, \cdots$
When $n>3$, the $n$-th non-wise number is $4 n-10$.
Therefore, the 2009th non-wise number is
$$
4 \times 2009-10=8026 \text {. }
$$