Definition:Friedman Number

Definition
A Friedman number (base $n$) is a (positive) integer which is the result of an expression in base $n$ arithmetic which contains exactly its digits.

The expression is subject to the following constraints:
 * $(1): \quad$ The arithmetic operators $+$, $-$, $\times$, $\div$ and exponentiation are the only operators which are allowed.
 * $(2): \quad$ Parentheses are allowed, but only in order to override the default operator precedence, otherwise every number would trivially be Friedman by $n = (n)$.
 * $(3): \quad$ Leading zeroes are not allowed, otherwise other numbers would trivially be Friedman by, for example, $011 = 10 + 1$.

Examples
The first few base $10$ Friedman numbers are as follows: