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Thue Constant

The base-2 Transcendental Number


where the $n$th bit is 1 if $n$ is not divisible by 3 and is the complement of the $(n/3)$th bit if $n$ is divisible by 3. It is also given by the Substitution Map
$\displaystyle 0$ $\textstyle \to$ $\displaystyle 111$  
$\displaystyle 1$ $\textstyle \to$ $\displaystyle 110.$  

In decimal, the Thue constant equals 0.8590997969....

See also Rabbit Constant, Thue-Morse Constant

© 1996-9 Eric W. Weisstein