HAPPY NUMBER 😁

A happy number is a positive integer that, when a series of mathematical operations is applied, eventually becomes number 1. The sequence of operations is defined as follows:

1. The initial positive integer is taken.
2. The sum of the square digits is calculated.
3. Step 2 is repeated with the result obtained in the previous step.
4. The process continues to be repeated until number 1 is obtained or a cycle is detected.

Examples of happy numbers

Some examples of happy numbers are:

- 7: 7 → 49 → 97 → 130 → 10 → 1
- 10: 10 → 1 → 1
- 13: 13 → 10 → 1 → 1
- 19: 19 → 82 → 68 → 100 → 1 → 1

Properties of happy numbers

Happy numbers have some interesting properties:

- The sequence of operations always ends in 1 or a cycle.
- The sequence of operations can be very long before finishing in 1 or a cycle.
- An efficient algorithm is not known to determine whether a number is happy or not.