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A077772 Continued fraction expansion of the ternary Champernowne constant.

%I A077772 #39 Feb 16 2025 08:32:48
%S A077772 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,
%T A077772 2,1,3,1,10,1,21,1,1,4,3,577,1,
%U A077772 1079268324684171943515797470873767312825026176345571319042096689270,1,1,1,3,4,21,3,1,9,1
%N A077772 Continued fraction expansion of the ternary Champernowne constant.
%H A077772 John K. Sikora, <a href="/A077772/b077772.txt">Table of n, a(n) for n = 0..2061</a> (terms n = 0..1155 from Robert G. Wilson v)
%H A077772 J. K. Sikora, <a href="https://drive.google.com/file/d/0B2oQudZQvHfSV2NudWYzUVpCMHM/edit?usp=sharing">The first 2982556 terms of the CFE of the ternary Champernowne Constant (141 MB zipped)</a>
%H A077772 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TernaryChampernowneConstant.html">Ternary Champernowne Constant</a>
%t A077772 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 *)
%o A077772 (PARI) \p 10000
%o A077772 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
%o A077772 (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
%Y A077772 Cf. A054635 (ternary digits), A077771 (decimals).
%Y A077772 Cf. A030190, A066716, A066717: binary digits, decimals and continued fraction of the binary Champernowne constant; A033307: decimal Champernowne constant.
%K A077772 nonn,base,cofr
%O A077772 0,4
%A A077772 _Eric W. Weisstein_, Nov 15 2002