Let S(n) be the sum of the digits of a natural number n, e.g. S(168) = 15.

Call a number n "special" if it is evenly divisible by S(n), e.g. 36 is special because S(36) = 9 and 9 divides 36.

Prove that there cannot be a sequence of 22 consecutive numbers that are all special.

Bonus: Prove that there cannot be a sequence of 21 consecutive special numbers.