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23 May 2008

Thue-Morse Sequence

I was wondering - how many of you ever thought about the sequence 0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,...?

It's a sequence that's fun to try and recite (fun = fun for me, yeah I'm a geek I know). I just recently found out that my little sister Shira also independently "discovered" this sequence and enjoys reciting it from time to time.

Have any of you done so as well?

BTW, the lengthiest prefix of it I can quickly produce (in one or two attempts) without external aid is the first 112 elements:
0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,

1 comment:

Elmer said...
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