Squares whose Digits form Consecutive Decreasing Integers

Theorem
The sequence of integers whose squares have a decimal representation consisting of the concatenation of $2$ consecutive decreasing integers begins:
 * $91, 9079, 9901, 733 \, 674, 999 \, 001, 88 \, 225 \, 295, 99 \, 990 \, 001, \ldots$

Proof
We have:

They can be determined by inspection.

Also see

 * Squares whose Digits form Consecutive Integers
 * Squares whose Digits form Consecutive Increasing Integers