digital root

Given an integer m consisting of k digits d1,,dk in base b, let


then repeat this operationMathworldPlanetmath 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 bx is always 1 for any natural x, while the digital root of ybn (where y is another natural numberMathworldPlanetmath) is the same as the digital root of y. This should not be taken to imply that the digital root is necessarily a multiplicative functionMathworldPlanetmath.

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

Another way to calculate the digital root for m>b is with the formulaMathworldPlanetmathPlanetmath m-(b-1)m-1b-1.

Title digital root
Canonical name DigitalRoot
Date of creation 2013-03-22 15:59:34
Last modified on 2013-03-22 15:59:34
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 13
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A63
Synonym repeated digit sum
Synonym repeated digital sum
Defines additive persistence