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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