The sequence composed of 1s and 2s obtained by starting with the number 1, and picking subsequent elements to avoid repeating the longest possible substring. The first few terms are 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, ... (Sloane's A006345). The Sally sequence gives the length of the run that was avoided.

Sloane, N. J. A. Sequence A006345/M0126 in "The On-Line Encyclopedia of Integer Sequences."

Sloane, N. J. A. and Plouffe, S. Figure M0126 in The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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Weisstein, Eric W. "Linus Sequence." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LinusSequence.html