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Are there any known Khinchin reals for which the asymptotics of "average" of their coefficients seems experimentally known?

We can define a Khinchin Real and recall the definition of Khinchin's Constant A real number $r$ is a Khinchin real if given the simple continued fraction expansion of $r$ as $$ r = a_0 + \cfrac{1}{...
Sidharth Ghoshal's user avatar