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Homemultiplicative digital root

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# multiplicative digital root

Given an integer $m$ consisting of $k$ digits $d_{1},\dots,d_{k}$ in base $b$, let

$j=\prod_{{i=1}}^{{k}}d_{i},$ |

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

Defines:

multiplicative persistence

Synonym:

repeated digit product, repeated digital product

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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