Editing Prouhet–Thue–Morse constant (section)

==Appearances==

The Prouhet–Thue–Morse constant appears in [[probability]]. If a [[Formal language|language]] ''L'' over {0, 1} is chosen at random, by flipping a [[fair coin]] to decide whether each word ''w'' is in ''L'', the probability that it contains at least one word for each possible length is <ref>{{cite journal |last1=Allouche |first1=Jean-Paul |last2=Shallit |first2=Jeffrey |title=The Ubiquitous Prouhet–Thue–Morse Sequence |journal=Discrete Mathematics and Theoretical Computer Science |date=1999 |page=11 |url=http://www.cs.uwaterloo.ca/~shallit/Papers/ubiq.ps}}</ref>
:<math> p = \prod_{n=0}^{\infty}\left(1-\frac{1}{2^{2^n}}\right) = \sum_{n=0}^{\infty} \frac{(-1)^{t_n}}{2^{n+1}} = 2 - 4 \tau = 0.35018386544\ldots</math>