login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A030167 Continued fraction expansion of Champernowne constant. 8
0, 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(18) = 457540111...783010987 has 166 digits.

a(41) = 445735380...113172423 has 2504 digits. - Harvey P. Dale, May 23 2015

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 number 0.123456789101112131415... whose base-10 representation character string is obtained by appending to the string "0." the base-10 representation character strings of all positive integers successively.

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: A053463 A073636 A113521 * A010767 A064734 A090929

Adjacent sequences:  A030164 A030165 A030166 * A030168 A030169 A030170

KEYWORD

nonn,cofr,nice,easy

AUTHOR

Eric W. Weisstein

EXTENSIONS

Edited by Daniel Forgues, Apr 01 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 30 04:42 EDT 2017. Contains 284296 sequences.