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471 series/series.32.p




Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

471 series/series.32.p


0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1

series/series.32.s

0 -> 1 01 -> 10 0110 -> 1001 01101001 -> 10010110
Recursively append the inverse.

This sequence is known as the Morse-Thue sequence. It can be defined
non-recursively as the nth term is the mod 2 count of 1s in n written
in binary:
0->0 1->1 10->1 11->0 100->1 101->0 110->0 111->1 etc.

Reference:
Dekking, et. al., "Folds! I,II,III"
The Mathematical Intelligencer, v4,#3,#4,#4.

 

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