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A030167
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Continued fraction expansion of the Champernowne constant 0.1234567891011121314...
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10
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0, 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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This is the continued fraction of the number 0.123456789101112131415... whose decimals are obtained by concatenating the base-10 representations of all positive integers.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,cofr,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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