The Sally sequence gives the sequence of lengths of the repetitions which are avoided in the Linus sequence. The first few terms are 0, 1, 1, 2, 1, 3, 1, 1, 3, 2, 1, 6, 3, 2, ... (Sloane's A006346).

Sloane, N. J. A. Sequence A006346/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. "Sally Sequence." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SallySequence.html