While I was dealing with the Happy Number problem, I came across another question. Will after a certain finite iteration, the sum of squared digits of a number eventually become a single number.
For example: $23 \to 2^2 + 3^2 = 13 \to 1^2 + 3^2 = 10 \to 1^2 + 0^2 = 1$.
This is a single number. Is it true for every number ? And are there any explanation for it ? Thanks everyone.