Puzzle #14: Sets of Numbers

The positive integers have been divided up into three sets. Each positive integer is in only one of the sets. What is the rule for membership in each set?

A = {1, 5, 8, 10, 13, 17, 22, 24, 26, 29, …}
B = {2, 4, 6, 9, 11, 15, 18, 20, 23, 27, …}
C = {3, 7, 12, 14, 16, 19, 21 25, 28, 30, …}

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, September 11, 2013 at noon Pacific Time. I will post the answer shortly after.