# digit sum

Given an integer $m$ consisting of $k$ digits $d_{1},\dots,d_{k}$ 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 $j 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.

Title digit sum DigitSum 2013-03-22 16:22:53 2013-03-22 16:22:53 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Definition msc 11A63