Self number

In number theory, a self number or Devlali number in a given number base ${\displaystyle b}$ is a natural number that cannot be written as the sum of any other natural number ${\displaystyle n}$ and the individual digits of ${\displaystyle n}$. 20 is a self number (in base 10), because no such combination can be found (all ${\displaystyle n<15}$ give a result less than 20; all other ${\displaystyle n}$ give a result greater than 20). 21 is not, because it can be written as 15 + 1 + 5 using n = 15. These numbers were first described in 1949 by the Indian mathematician D. R. Kaprekar.^[1]