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.