Prouhet-Thue-Morse constant

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

$$\tau =\sum _{i=0}^{\mathrm{\infty }}\frac{t_i}{2^{i+1}}=0.412454033640\mathrm{\dots }$$

where $t_i$ is the Prouhet-Thue-Morse sequence

Another expression, not in of $t_i$, is

$$\tau =\frac{1}{2}-\frac{1}{4}\prod _{n=0}^{\mathrm{\infty }}(1-2^{-2^i})$$

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

Title	Prouhet-Thue-Morse constant
Canonical name	ProuhetThueMorseConstant
Date of creation	2013-03-22 14:28:23
Last modified on	2013-03-22 14:28:23
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	7
Author	mathcam (2727)
Entry type	Definition
Classification	msc 11J81
Classification	msc 11B85
Related topic	ProuhetThueMorseSequence
Defines	Thue-Morse constant