Remainder 1, 1, 2,3, 1, 0, 1, 2,3, 1, 0, ...
Cycle every six numbers, and the remainder is 1, 1, 2,3, 1, 0,
2006/6=334…2, corresponding to the number 2 in the cycle.
Divide the 2006th number by 4, and the remainder is 1.