Self-Descriptive Number Fixed-Point Function

A self-descriptive number in base 10 is a 10-digit number x, the digits of
x being numbered from most to least significant as d0,…,d9, such that di
represents the quantity of the digit i in the decimal representation of x. See Weisstein, Eric W. “Self-Descriptive Number.” From MathWorld, a Wolfram Web Resource.

A number-theoretic function which is the base-10 fixed point of the self-describing number is presented in this paper.