The first few convergents from the continued fraction expansion of the MRB constant are 0,1/5,3/16,31/165,34/181 and 65/346. If you were to use those convergents as terms of a generalized continued fraction, it would represent, approximately,

0+1/(0.20+1/(0.1875+1/(0.1878787+1/(0.187845+1/0.187861))))=1.83346...

Then construct a large generalized continued fraction from all of the convergents of the MRB constant; and it will represent, approximately,

m2=0.90025825591255519.

Then construct a large generalized continued fraction from all of the convergents of m2; and it will represent, approximately,

m3=0.607305254830648711246.

Then construct a large generalized continued fraction from all of the convergents of m3; and it will represent, approximately,

m4=0.5470849624553981928.

Then construct a large generalized continued fraction from all of the convergents of m4; and it will represent, approximately, 

m5=0.55707672427687520312.

Then construct a large generalized continued fraction from all of the convergents of m5; and it will represent, approximately

m6=0.5557189461711235196678.

Then construct a large generalized continued fraction from all of the convergents of m6; and it will represent, approximately

0.5557189461711235196678.

Thus we are left with a rapidly converging constant with a continued fraction representation of  

{0,1,1,3,1,61,1,2,1,1,8,2,1,4,1,2,1,3,4,2,1,3,1,2,1,3,2,9,3,4,1,6}

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