digit sum

Given an integer $m$ consisting of $k$ digits $d_1,\mathrm{\dots },d_k$ in base $b$, let

$$j=\sum _{i=1}^k{d}_i,$$

then $j$ is the digit sum of $m$. Iterating this operation on the digits of $j$ until gives the digital root or repeated digit sum of $m$. The digit sum and digital root of a number are the same only if the additive persistence of the digital root is 1.