Prouhet-Thue-Morse constant

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The Prouhet-Thue-Morse constant is the number $\tau$ whose binary expansion is the Prouhet-Thue-Morse sequence. That is,

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

where $t_{i}$ is the Prouhet-Thue-Morse sequence

Another expression, not in terms of $t_{i}$ , is

\tau=\frac{1}{2}-\frac{1}{4}\prod_{{n=0}}^{{\infty}}(1-2^{{-2^{i}}})

The number $\tau$ has been shown to be transcendental.

Defines:

Thue-Morse constant

Type of Math Object:

Definition

Major Section:

Reference