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Homedigital root

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# digital root

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 repeat this operation on the digits of $j$ until $j<b$. This stores in $j$ the digital root of $m$. The number of iterations of the sum operation is called the additive persistence of $m$.

The digital root of $b^{x}$ is always 1 for any natural $x$, while the digital root of $yb^{n}$ (where $y$ is another natural number) is the same as the digital root of $y$. This should not be taken to imply that the digital root is necessarily a multiplicative function.

The digital root of an integer of the form $n(b-1)$ is always $b-1$.

Defines:

additive persistence

Synonym:

repeated digit sum, repeated digital sum

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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