Definition:Digital Root

Definition
Let $n \in \Z: n \ge 0$.

Let $n$ be expressed in base $b$ notation.

Let $n_1 = \map {s_b} n$ be the digit sum of $n$ to base $b$.

Then let $n_2 = \map {s_b} {n_1}$ be the digit sum of $n_1$ to base $b$.

Repeat the process, until $n_m$ has only one digit, that is, that $1 \le n_m < b$.

Then $n_m$ is the digital root of $n$ to the base $b$.

Also see

 * Existence of Digital Root