This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A030167 #41 Feb 16 2025 08:32:35
%S A030167 0,8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15
%N A030167 Continued fraction expansion of the Champernowne constant 0.1234567891011121314...
%C A030167 The next term, a(18) = 457540111...783010987 has 166 digits.
%C A030167 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
%C A030167 a(40) = 445735380...113172423 has 2504 digits. - _Harvey P. Dale_, May 23 2015, index corrected by _M. F. Hasler_, Oct 25 2019
%H A030167 Harry J. Smith, <a href="/A030167/b030167.txt">Table of n, a(n) for n=0..39</a> (see the a-file for further terms)
%H A030167 Harry J. Smith, <a href="/A030167/a030167.txt">Table of n, a(n) for n=0..161</a>
%H A030167 H. Havermann, <a href="http://chesswanks.com/pxp/cfc.html">13522 (less the 3 largest) terms (2 MB file)</a>
%H A030167 J. K. Sikora, <a href="https://docs.google.com/file/d/0B_ZIuCD9HzQtNnlLQUdIYTRXY2M/edit">Champernowne's Constant CFE Coefficients to HWM #12 (789 MB unzipped)</a>
%H A030167 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChampernowneConstant.html">Champernowne Constant.</a>
%H A030167 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A030167 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A030167 This is the continued fraction of the number 0.123456789101112131415... whose decimals are obtained by concatenating the base-10 representations of all positive integers.
%t A030167 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 ]
%t A030167 chcon=Module[{con=FromDigits[Flatten[IntegerDigits/@Range[250]]]}, N[con/10^IntegerLength[con],IntegerLength[con]]]; ContinuedFraction[ chcon,19] (* _Harvey P. Dale_, Sep 18 2011 *)
%t A030167 ContinuedFraction[N[ChampernowneNumber[10],10000]] (* _Harvey P. Dale_, May 23 2015 *)
%o A030167 (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
%Y A030167 Cf. A033307, A033435.
%K A030167 nonn,cofr,nice
%O A030167 0,2
%A A030167 _Eric W. Weisstein_
%E A030167 Edited by _Daniel Forgues_, Apr 01 2010, _M. F. Hasler_, Oct 25 2019