Teaser 2963: A result

From The Sunday Times, 7th July 2019 [link]

For any number, I square the digits and then add the resulting numbers. If necessary, I keep repeating the process until I end up with a single digit, called the result. For example: 142 gives 1 + 16 + 4 = 21 which then gives 4 + 1 = 5, the result.

I have written down a two-digit number. If I tell you one of the digits [the key digit], you should be able to work out the result.

I then use a 3rd digit to get a three-digit number. The result of that number happens to be the key digit.

In increasing order, what are the three digits?