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How many squares must a binary sequence contain? (English) Zbl 0816.11007
Electron. J. Comb. 2, Research paper R2, 9 p. (1995); printed version J. Comb. 2, 47-55 (1995).
Summary: Let $$g(n)$$ be the length of a longest binary string containing at most $$n$$ distinct squares (two identical adjacent substrings). Then $$g(0)=3$$ (010 is such a string), $$g(1)= 7$$ (0001000) and $$g(2)= 18$$ (010011000111001101). How does the sequence $$\{g(n)\}$$ behave? We give a complete answer.

##### MSC:
 11A67 Other number representations 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
##### Keywords:
length; longest binary string; distinct squares
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