Help me find equation of this graph I need to find equations of this list: $[1,1,1,0,0,0,1,1,1,0,0,0, ...]$ (it's periodic)
The closest equation I've got is $\left\lceil \sin (\frac{\pi}{3}x)\right\rceil $, which looks like this:
  _   _   _
_| |_| |_| |_

But I need it to look like this:
  _   _   _
_/ \_/ \_/ \_

Can you help me?
 A: I'd use
$$\max\left(0,\min\left(\frac12-\frac3{\pi}\arcsin\left(\cos\left(\frac{\pi}{3}(x+1)\right)\right),1\right)\right)$$
A: You may try the simple function 
$$f(x)=|(x-s) \bmod 6 -3|-1$$
(the 'shift' $s$ is $0$ for the first list , $1$ for the second and so on...)
by replacing values over $1$ by $1$ and under $0$ by $0$
Or don't you allow tests?
A: It seems you are looking for the left shift operator $S_l$:
$$ S_l: (x_j)_{j=1}^{\infty}\mapsto (x_j)_{j=2}^{\infty} $$
It simply crosses out the first component of the sequence. You can write your whole sequence $(x^{(n)})_{n=1}^{\infty}$of "lists" as powers of this operator $S_l$: $x^{(n)} = S^{n-1}_lx^{(1)}$
I hope this helps.
A: See http://oeis.org/A088911 ... The $n$th term ($n = 0, 1, 2, ...)$ of the sequence $1^k 0^k 1^k 0^k ...$ is 
$$a(n,k) = \left\lfloor \frac{(n+k)\mod 2k}{k}\right\rfloor$$
so your function can be written 
$$f(n) = a(n,3) = \left\lfloor \frac{(n+3)\mod 6}{3}\right\rfloor.$$
The linked article also shows other ways to write it.
