jmc

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:

$$f(i,j)=\{\begin{array}{ll}{\text{mod}}_5(j+1)& \text{ if }i=0\text{ and }0\le j\le 4\text{,}\\ f(i-1,1)& \text{ if }i\ge 1\text{ and }j=0\text{, and}\\ f(i-1,f(i,j-1))& \text{ if }i\ge 1\text{ and }1\le j\le 4.\end{array}$$What is $f(2015,2)$?