The constant also called the Parity Constant and defined by

(1) |

The Thue-Morse constant can be written in base 2 by stages by taking the previous iteration , taking the complement
, and appending, producing

(2) |

This can be written symbolically as

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

The Sequence (Sloane's A010060) is known as the Thue-Morse Sequence.

**References**

Allouche, J. P.; Arnold, A.; Berstel, J.; Brlek, S.; Jockusch, W.; Plouffe, S.; and Sagan, B.
``A Relative of the Thue-Morse Sequence.'' *Discr. Math.* **139**, 455-461, 1995.

Allouche, J. P. and Shallit, J. In preparation.

Beeler, M.; Gosper, R. W.; and Schroeppel, R. *HAKMEM.* Cambridge, MA: MIT
Artificial Intelligence Laboratory, Memo AIM-239, Item 122, Feb. 1972.

Dekking, F. M. ``Transcendence du nombre de Thue-Morse.'' *Comptes Rendus de l'Academie des Sciences de Paris* **285**, 157-160, 1977.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/cntfrc/cntfrc.html

Sloane, N. J. A. Sequences A010060, A014571, and A014572 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

© 1996-9

1999-05-26