An irrational number 
can be called GK-regular (defined here for the first time)
if the distribution of its continued fraction coefficients is the Gauss-Kuzmin
distribution. An irrational number that is not GK-regular is said to be GK-irregular.
It has been shown that all real numbers except for a set of measure zero are GK-regular.
Classes of GK-irregular numbers include rational and real quadratic numbers and numbers of the form 
where 
is a nonzero integer. Most widely-studied
real numbers not of one of these forms, such as 
and algebraic numbers of degree greater than 2, are strongly
suspected to be GK-regular based on numerical evidence, although no proof is known.
The situation is much the same for normal and absolutely normal numbers.
