The Sally sequence records the largest length of a block 
for which appending the rejected next symbol would give the
terminal repetition 
in the construction of the Linus sequence (Balister
et al. 2010). Its initial term is 0. The first few terms are 0, 1, 1, 2, 1,
3, 1, 1, 3, 2, 1, 6, 3, 2, ... (OEIS A006346).
Sally Sequence
See also
Linus SequenceExplore with Wolfram|Alpha
References
Balister, P.; Kalikow, S.; and Sarkar, A. "The Linus Sequence." Combinatorics, Probability and Computing 19, 21-46, 2010. https://doi.org/10.1017/S0963548309990198.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, CA: Academic Press, 1995.Referenced on Wolfram|Alpha
Sally SequenceCite this as:
Weisstein, Eric W. "Sally Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SallySequence.html