# 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 |