
Kimberling, Clark
Special M ★★
Author(s): Kimberling
Let denote the golden ratio,
and let
denote the floor function. For fixed
, let
, let
, and let
. We can expect
to have about the same growth rate as
.
Conjecture Prove or disprove that for every fixed
, as
ranges through all the positive integers, there is a number
such that
takes each of the values
infinitely many times, and
. (Can you formulate
as a function of
? Generalize for other numbers
?)









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