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# Prouhet-Thue-Morse constant

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

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

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

Related:

ProuhetThueMorseSequence

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11J81*no label found*11B85

*no label found*

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new image: plot W(t) = P(waiting time <= t) by robert_dodier

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier