An integer that in a given base lacks a digitaddition generator.

Consider, for example, the integer 41 in base 10. It can be expressed as 34 + 3 + 4. For 42, however, there is no such digitaddition, hence it is a self number.

If , all odd will be self numbers.

Though self numbers form a small proportion of most ranges of consecutive integers, there are infinitely many of them: The recurrence relation (with if and otherwise) will give an incomplete though infinite list of self numbers.

Reference

Kaprekar, D. R. The Mathematics of New Self-Numbers. Devaiali, 1963: 19 - 20