Thue–Morse sequence
= Thue–Morse sequence
{c}
{title2=$t_n=s_2(n)\bmod2$}
{wiki}
Here $s_2(n)$ is the sum of the <binary digits> of the nonnegative <integer> $n$. The sign version is $f(n)=(-1)^{s_2(n)}$. Concatenating binary digits gives $f(a2^j+r)=f(a)f(r)$ for $0\le r<2^j$. It supplies cancellation controlled by binary blocks rather than multiplicative factorization.