Also, the interviewer didn't even know his own question.

As I understand it, you are taking the sequence

n -> (sum of the squares of the digits of n)

First, the sequence never diverges to infinity. For example, 9999999999 -> 9*81.

Second, not all numbers converge to 1. There is a stable cycle that does not include one.

Consider

4 -> 16 -> 37 -> 56 -> 61 -> 37 -> ...

So, any positive integer either

1. Converges to 1

2. Converges to the stable cycle I just mentioned above.

So the interviewer should be fired for not understanding the question he was asking.