A self number (or Colombian number) is one that no other number generates under the map \(m \mapsto m + \text{digitsum}(m)\). For instance, 21 is not self because 15 + (1+5) = 21; but nothing generates 20, so 20 is self.
Introduced by the Indian recreational mathematician D. R. Kaprekar (of Kaprekar-number and 6174 fame). In base 10 there are infinitely many self numbers, with a regular pattern in their distribution — roughly 10% of integers are self. The smallest self primes are 3, 5, 7, 31, 53, 97, 211, 233, 277.