==> arithmetic/digits/sum.of.digits.s <==
let X = 4444^4444

sod(X) <= 9 * (# of digits) < 145900
sod(sod(X)) <= sod(99999) = 45
sod(sod(sod(X))) <= sod(39) = 12

but sod(sod(sod(X))) = 7 (mod 9)

thus sod(sod(sod(X))) = 7