NO-ABEL 2011 Problem 1

Let $n$ be the number that is produced by concatenating the numbers $1, 2,... , 4022$ , that is, $n = 1234567891011...40214022$ . a. Show that $n$ is divisible by $3$ . b. Let $a_1 = n^{2011}$ , and let $a_i$ be the sum of the digits of $a_{i-1}$ for $i > 1$ . Find $a_4$