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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.
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