Suppose we have a sequence of numbers, $$t_n$$
Such that $$t_{2n} = t_n$$
and
$$t_{2n+1} = 1 - t_n$$
Also, $$t_0 = 1$$
Is this sequence periodic?
I have found that the sequence of numbers comprise just of 1’s and 0’s but I couldn’t find an exact proof to whether it is periodic or not.