$1 \cdot 35$ A four-digit number is composed of four consecutive digits in sequence. If the first two digits from the left are swapped, the resulting number is a perfect square. Find the four-digit number.

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[Solution] Let the thousand's digit of the required four-digit number be $a$, then the hundred's digit, ten's digit, and unit's digit are $a+1, a+2$, and $a+3 (1 \leqslant a \leqslant 6)$ or $a-1, a-2$, and $a-3 (3 \leqslant a \leqslant 9)$.
From the problem, we have
$$
(a+1) \times 1000 + a \times 100 + (a+2) \times 10 + (a+3) = 1111a + 1023
$$

is a perfect square, where $1 \leqslant a \leqslant 6$,
or $(a-1) \times 1000 + a \times 100 + (a-2) \times 10 + (a-3) = 1111a - 1023$ is a perfect square, where $3 \leqslant a \leqslant 9$.
By direct verification, 3456 is the required number.