Question: I need a function that maps natural numbers (starting from zero) into the series [1, 0, 2, 1, 0, 2, 1, 0, 2, ...], i.e.:  

f(0) = 1  

f(1) = 0  

f(2) = 2  

f(3) = 1  

f(4) = 0  

f(5) = 2  

...

The function f(x) = mod(x, 3) gives the series [0, 1, 2, 0, 1, 2, ...], but I can't come up with a function to get the series I want.

Answer: 
Take it one step at a time.

f(x) = mod(x, 3) gives the series [0, 1, 2, 0, 1, 2, ...]

f(x) = mod(x + 1, 3) shifts that to [1, 2, 0, 1, 2, 0, ...]

f(x) = 2 - mod(x + 1, 3) is a winner [1, 0, 2, 1, 0, 2, ...]
$$f(x)=1-\frac2{\sqrt3}\sin\frac{2\pi x}3$$