Problem Statement

The digital root,

X

{\displaystyle X}

, of a number,

n

{\displaystyle n}

, is calculated: The additive persistence is the number of summations required to obtain the single digit. The task is to calculate the additive persistence and the digital root of a number, e.g.: The digital root may be calculated in bases other than 10.

Let's start with the solution:

fcn sum(n,b){ n.split(b).sum(0) }
fcn droot(n,b=10,X=0) // -->(digital root, additive persistence)
   { if(n

droot(627615)
droot(39390)
droot(588225)
droot(393900588225)
droot(7,2)
droot(0x7e0,16)