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 A030167 Continued fraction expansion of the Champernowne constant 0.1234567891011121314... 9
 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 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; f[n_Integer] := 10^(Floor[Log[10, n]] + 1)*f[n - 1] + n; ContinuedFraction[ N[ f/ 10^(Floor[ Log[10, f ]] + 1), Floor[ Log[10, f ]] + 1], 19 ] chcon=Module[{con=FromDigits[Flatten[IntegerDigits/@Range]]}, N[con/10^IntegerLength[con], IntegerLength[con]]]; ContinuedFraction[ chcon, 19] (* Harvey P. Dale, Sep 18 2011 *) ContinuedFraction[N[ChampernowneNumber, 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 AUTHOR EXTENSIONS Edited by Daniel Forgues, Apr 01 2010, M. F. Hasler, Oct 25 2019 STATUS approved

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Last modified July 3 17:50 EDT 2020. Contains 335418 sequences. (Running on oeis4.)