OFFSET
0,2
COMMENTS
The next term, a(18) = 457540111...783010987 has 166 digits.
It is followed by a(19 .. 39) = (6, 1, 1, 21, 1, 9, 1, 1, 2, 3, 1, 7, 2, 1, 83, 1, 156, 4, 58, 8, 54). - M. F. Hasler, Oct 25 2019
a(40) = 445735380...113172423 has 2504 digits. - Harvey P. Dale, May 23 2015, index corrected by M. F. Hasler, Oct 25 2019
LINKS
Harry J. Smith, Table of n, a(n) for n=0..39 (see the a-file for further terms)
Harry J. Smith, Table of n, a(n) for n=0..161
H. Havermann, 13522 (less the 3 largest) terms (2 MB file)
Eric Weisstein's World of Mathematics, Champernowne Constant.
G. Xiao, Contfrac
EXAMPLE
This is the continued fraction of the number 0.123456789101112131415... whose decimals are obtained by concatenating the base-10 representations of all positive integers.
MATHEMATICA
f[0] = 0; f[n_Integer] := 10^(Floor[Log[10, n]] + 1)*f[n - 1] + n; ContinuedFraction[ N[ f[211]/ 10^(Floor[ Log[10, f[211] ]] + 1), Floor[ Log[10, f[211] ]] + 1], 19 ]
chcon=Module[{con=FromDigits[Flatten[IntegerDigits/@Range[250]]]}, N[con/10^IntegerLength[con], IntegerLength[con]]]; ContinuedFraction[ chcon, 19] (* Harvey P. Dale, Sep 18 2011 *)
ContinuedFraction[N[ChampernowneNumber[10], 10000]] (* Harvey P. Dale, May 23 2015 *)
PROG
(PARI) { default(realprecision, 6000); x=0; y=1; d=10.0; e=1.0; n=0; while (y!=x, y=x; n++; if (n==d, d=d*10); e=e*d; x=x+n/e; ); x=contfrac(x); for (n=1, 160, write("b030167.txt", n-1, " ", x[n])); write("b030167.txt", "160 1"); write("b030167.txt", "161 1"); } \\ Harry J. Smith, Apr 18 2009
CROSSREFS
KEYWORD
nonn,cofr,nice
AUTHOR
EXTENSIONS
Edited by Daniel Forgues, Apr 01 2010, M. F. Hasler, Oct 25 2019
STATUS
approved