Binary words with a given Diophantine exponent

We prove that every real number @x>=1 is the Diophantine exponent of some binary word @w. More precisely, we show that Dio(@w)[email protected] for @w=10^k^"^110^k^"^210^k^"^3..., where k"n=[@x^n] for @x>=2,k"n=[@n^n] with @n=([email protected][email protected]@x^2+1)/([email protected]) for 1<@x<2, and k"n=n for @x=1.

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