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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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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

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new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag