multiplicative digital root

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

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

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

Title	multiplicative digital root
Canonical name	MultiplicativeDigitalRoot
Date of creation	2013-03-22 16:00:42
Last modified on	2013-03-22 16:00:42
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	4
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A63
Synonym	repeated digit product
Synonym	repeated digital product
Defines	multiplicative persistence