Self Number Calculator

What is a Self Number?

A self number, also known as a Colombian number, is a natural number that cannot be expressed as the sum of any other natural number and the sum of its digits. For a number \( n \) to be a self number, there must be no integer \( m \) such that \( n = m + S(m) \), where \( S(m) \) is the sum of the digits of \( m \).

How to Determine if a Number is a Self Number

1. Check if Natural: Ensure the number is a natural number.
2. Iterative Validation: For all natural numbers \( m \) less than \( n \):
   • Compute \( S(m) \), the sum of the digits of \( m \).
   • Calculate \( m + S(m) \).
   • If any \( m \) satisfies \( m + S(m) = n \), then \( n \) is not a self number.
3. Conclusion: If no such \( m \) is found after checking all possibilities, \( n \) is a self number.

For example: Is 21 a Self Number?

The First 100 Self Numbers