The constant is defined at http://mathworld.wolfram.com/MRBConstant.html. Additional usage is found on a Google Scholar ( https://scholar.google.com/scholar?q=%22MRB+constant%22 ).

In the first more than 3 million digits there is no termination or period of digits,. On top of that, the only pattern of its simple continued fraction is the trivial pattern that it follows its own pattern. I'm not sure how to determine how approximable it is through its convergents -- that might help me.

I'm attaching its first 3,014,991 digits.