Happy number

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).

More formally, given a number ${\displaystyle n=n_{0}}$, define a sequence ${\displaystyle n_{1}}$, ${\displaystyle n_{2}}$, ... where ${\displaystyle n_{i+1}}$ is the sum of the squares of the digits of ${\displaystyle n_{i}}$. Then n is happy if and only if there exists i such that ${\displaystyle n_{i}=1}$.

...
Wikipedia