Dan Asimov wrote:
so a natural question is whether the CF quotients have the "expected" distribution...
Bill Gosper wrote (pi cf record):
Has anyone listed the largest terms in Hans's data? The GM?
I just figured out GM = geometric mean. :) Without getting into actual number counts, all is as expected. I calculated the geometric mean of my 180 million terms at the end of October 2002. In Mathematica, using 500-digit accuracy for the multiplications, the GM came to Khinchin + 0.00023431342958765. It should be noted that the GM-drift above and below Khinchin's constant is erratic and the closest we have come to it was much, much earlier - for 4497058 terms of the (fractional part of the) continued fraction. I have a graph of the evolving GM in this neighborhood here: http://chesswanks.com/pxp/Images/4497058.gif See also Sloane's A059101, a sequence I imagine to be infinite: http://www.research.att.com/~njas/sequences/A059101