The phrase "neon number" is sometimes used for a number where: square the number, add the digits of that in base 10, and you get the original number.
So, 9 is a neon number (-> 81, 8+1, 9)
Indeed it is usually said there are only three neon numbers (0, 1, and 9).
Surprisingly I couldn't google any proof of this. (All the numbers up to a few billion have been trivially tested.)
Is there a proof?
And angularly, are "neon numbers" of any value or interest at all, or is it just a quirky thing?