Continued fraction expansion of the Champernowne number.
From: Simon Plouffe <simon.plouffe@sympatico.ca>
To: NMBRTHRY@LISTSERV.NODAK.EDU
Date: Sun, 13 Jan 2002 23:03:36 -0500


Hello,

for very large partial quotient try the continued
fraction expansion of the Champernowne number which is
0.1234567891011... the concatenation of the natural numbers.

beware : you will need to set the working precision to several
thousands digits before to get any reliable result.

The reason for the large p.q. is simple since (for example)
10/81 = 0.12345678910 (almost), there is a rational number for
the concatenation of .10111213....9899 as well, all this to say ;
the Champernowne number is almost rational and as the number of
digits increase it gets closer and closer to it, the p.q are
unbounded.


see some results at www.mathworld.com under Champernowne.


Simon Plouffe
plouffe@math.uqam.ca