# Digital Roots

The digital root is defined as the sum of all the digits of a number, $$n$$.

More concretely, suppose that,

$n = d_0 + d_1 b + d_2 b^2 + \cdots + d_n b^n\, ,$

therefore the digits are given as $$\{ d_0, d_1, d_2, \dots, d_n \}$$ and so the digital root, $$D$$, is defined by,

$D \equiv \sum_{i=0}^n d_i$
function digitalroot(n::Int)
while (n = sum(digits(n))) > 9 end
return n
end

or using recursion,

function digitalroot(n::Int)
n < 10 && return n
return digitalroot(n |> digits |> sum)
end