Australian AMC 2012 - Intermediate Question 30

Terry has invented a new way to extend lists of numbers. To Terryfy a list such as $[1,8]$ he creates two lists $[2,9]$ and $[3,10]$, where each term is one more than the corresponding term in the previous list, and then joins the three lists together to give $[1,8,2,9,3,10]$. If he starts with a list containing one number $[0]$ and repeatedly Terryfies it he creates the list

$$[0,1,2,1,2,3,2,3,4,1,2,3,2,3,4,3,4,5,2,3,4,\ldots].$$

What is the 2012th number in this Terryfic list?