Michael's number

For positive integers $$b>1$$ and $$n\ge 1,$$ let $$f_n(b)$$ be the largest number (in decimal notation) that has $$n$$ digits when expressed in base $$b$$. Find the sum of all possible $$n$$ such that there exists a value of $$b$$ that satisfies $$f_n(b) = 4095.$$

This problem is posed by Michael T.

Details and assumptions

You may choose to read Number Base Representation.

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