Is the Prouhet-Thue-Morse constant transcendental in any integer base $b>2$?

Question

The Prouhet-Thue-Morse constant, defined as

$$ \tau =\sum _{{i=0}}^{{\infty }}{\frac {t_{i}}{2^{{i+1}}}}=0.412454033640\ldots $$

where the $t_i$ are elements of the Thue-Morse sequence, is transcendental. But is

$$ \tau_b =\sum _{{i=0}}^{{\infty }}{\frac {t_{i}}{b^{{i+1}}}} $$

also transcendental, for $b>2$?

Answer 1

The answer is of course yes, see the MaothOverflow post here.