Freeflows

Recursive Function Evaluation 3

For every positive integer $ n $, let $ \text{mod}_5 (n) $ be the remainder obtained when $ n $ is divided by 5. Define a function $ f: \{0,1,2,3,\dots\} \times \{0,1,2,3,4\} \to \{0,1,2,3,4\} $ recursively as follows: \[f(i,j) = \begin{cases}\text{mod}_5 (j+1) & \text{ if } i = 0 \text{ and } 0 \le j \le 4 \text{,}\\ f(i-1,1) & \text{ if } i \ge 1 \text{ and } j = 0 \text{, and} \\ f(i-1, f(i,j-1)) & \text{ if } i \ge 1 \text{ and } 1 \le j \le 4.\end{cases}\]What is $ f(2015,2) $?

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