The th term is defined to be the number of s in the binary expansion of , modulo 2. That is, if the number of s in the binary expansion of is even, and if it is odd.
The Prouhet-Thue-Morse sequence is an automatic sequence. It has been shown to be (no three consecutive identical blocks) and overlap-free i.e no sub-block of the form , where , when viewed as a word of infinite length over the binary alphabet .
The Thue-Morse sequence was independently discovered by P. Prouhet, Axel Thue, and Marston Morse, and has since been rediscovered by many others.
Allouche, J.-P.; Shallit, J. O. http://www.cs.uwaterloo.ca/ shallit/Papers/ubiq.psThe ubiquitous Prouhet-Thue-Morse Sequence [postscript]
Sloane, N. J. A. Sequence A010060, http://www.research.att.com/ njas/sequences/The On-Line Encyclopedia of Integer Sequences.
|Date of creation||2013-03-22 14:27:17|
|Last modified on||2013-03-22 14:27:17|
|Last modified by||Mathprof (13753)|