Self number

is a natural number that cannot be written as the sum of any other natural number

and the individual digits of

20 is a self number (in base 10), because no such combination can be found (all

give a result less than 20; all other

give a result greater than 20).

These numbers were first described in 1949 by the Indian mathematician D. R.

-self function for base

is the empty set.

For odd bases, all odd numbers are self numbers.

[2] The set of self numbers in a given base

is infinite and has a positive asymptotic density: when

is odd, this density is 1/2.

[3] For base 2 self numbers, see OEIS: A010061.

(written in base 10) The first few base 10 self numbers are: A self prime is a self number that is prime.