I recently had a thought about numbers having the following properties:
- A number is two less than the perfect square.
- The sum of a number's digits is equal exactly to the square root of that square.
The example of such number is $23$, because $23=25-2=5^2-2=(2+3)^2-2$.
Is there a known sequence of such numbers? If yes, does it have a special name?
As Ivan pointed out in the comments, this supposed "sequence" is finite (having only seven terms), and seems awfully contrived to have any real meaning.
Heropup also gave an outline of the proof to show the sequence has no other terms.
Perhaps there is some sort of background of the question that you need to inform us about.