In decimal notation, $\dfrac 1{81} = 0.01234567901234567901234\dots$

In analogy to this, we wish to find a fraction for which in hexadecimal notation $\dfrac 1{n} = 0.0123456789ABCDF0123456789ABCDF01\dots$ What is the value of $$n$$, expressed as a hexadecimal numeral?

Bonus: Generalize this for number base $$b$$.

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