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A077772
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Continued fraction expansion of the ternary Champernowne constant.
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7
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0, 1, 1, 2, 37, 1, 162, 1, 1, 1, 3, 1, 7, 1, 9, 2, 3, 1, 3068518062211324, 2, 1, 2, 6, 13, 1, 2, 1, 3, 1, 10, 1, 21, 1, 1, 4, 3, 577, 1, 1079268324684171943515797470873767312825026176345571319042096689270, 1, 1, 1, 3, 4, 21, 3, 1, 9, 1
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OFFSET
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0,4
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LINKS
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MATHEMATICA
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almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Take[ ContinuedFraction[ FromDigits[ {Array[almostNatural[#, 3] &, 20000], 0}, 3]], 100] (* Robert G. Wilson v, Jul 21 2014 *)
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PROG
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(PARI) \p 10000
t=0; r=0.; T=1; for(n=1, 1e6, d=#digits(n, 3); t+=d; T*=3^d; r+=n/T; if(t>20959, return)); v=contfrac(r); v[1..30] \\ Charles R Greathouse IV, Sep 23 2014
(PARI) A077772(b=3, t=1., s=b)={contfrac(sum(n=1, default(realprecision)*2.303/log(b)+1, n<s||s*=b; n*t/=s))} \\ First optional arg allows us to get the c.f. of C[b] for other bases. - M. F. Hasler, Oct 25 2019
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CROSSREFS
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Cf. A030190, A066716, A066717: binary digits, decimals and continued fraction of the binary Champernowne constant; A033307: decimal Champernowne constant.
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KEYWORD
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nonn,base,cofr
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AUTHOR
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STATUS
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approved
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