So, I *think* most of our hypothetical problems go away with a simple
adjustment to f(n):

f(n) = floor(log_M((n-1)/B))

Correct. And nice. :-)

Equivalently,
f(n) = ceil(log_M (n / B)). If f(n) = c, it means B*(M^(c-1)) < n <= B*(M^(c)).

So f(n) = 0 means n <= B.

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