The digital root of a nonnegative integer 
in an integer base 
is the digit obtained by repeatedly taking its digit
sum until a single digit remains. The number of digit sum steps is the additive
persistence of 
. The digital root of 0 is 0.
For example, the sequence obtained from the starting number 9876 in base 10 is (9876, 30, 3), so 9876 has an additive persistence
of 2 and a digital root of 3. The base-10 digital roots of the first few positive
integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, ... (OEIS A010888). The base-10 digital root 
of a positive integer 
can be computed without actually performing
the iteration using the simple congruence formula
 |  |  |
(1)
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 |  | ![1+[n-1 (mod 9)].](/images/equations/DigitalRoot/Inline11.svg) |
(2)
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