A030167 Continued fraction expansion of the Champernowne constant 0.1234567891011121314...

0, 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15

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)

J. K. Sikora, Champernowne's Constant CFE Coefficients to HWM #12 (789 MB unzipped)

Eric Weisstein's World of Mathematics, Champernowne Constant.

G. Xiao, Contfrac

Index entries for continued fractions for constants

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

Cf. A033307, A033435.

Sequence in context: A073636 A113521 A297537 * A010767 A334751 A289252

Adjacent sequences: A030164 A030165 A030166 * A030168 A030169 A030170

Keyword

nonn,cofr,nice,changed

Author

Eric W. Weisstein

Extensions

Edited by Daniel Forgues, Apr 01 2010, M. F. Hasler, Oct 25 2019

Status

approved