cp's OEIS Frontend

A066717 The continued fraction for the "binary" Champernowne constant.

%I A066717 #30 Feb 16 2025 08:32:45
%S A066717 0,1,6,3,1,6,5,3,3,1,6,4,1,3,298,1,6,1,1,3,285,7,2,4,1,2,1,2,1,1,
%T A066717 4534532,1,4,5,1,2,1,7,1,16,1,4,1,5,5,1,5,1,4,1,2,1,5,3,2,38,2,12,1,
%U A066717 15,2,6,3,30,4682854730443938,1,1,68,1,6,5,4,4,1,2,1,1,1,1,2,22,1,2,7,1,2
%N A066717 The continued fraction for the "binary" Champernowne constant.
%H A066717 Robert G. Wilson v, <a href="/A066717/b066717.txt">Table of n, a(n) for n = 0..1000</a>
%H A066717 J. K. Sikora, <a href="https://drive.google.com/file/d/0B2oQudZQvHfSYkNyUndfNzJJaUE/edit?usp=sharing">The first 98093504 CFE coefficients of the binary Champernowne Constant (231 MB zipped)</a>
%H A066717 Eric E. Weisstein, <a href="https://mathworld.wolfram.com/BinaryChampernowneConstant.html">Binary Champernowne Constant</a>
%t A066717 a = {}; Do[a = Append[a, IntegerDigits[n, 2]], {n, 1, 10^3} ]; ContinuedFraction[ N[ FromDigits[ {Flatten[a], 0}, 2], 500]]
%t A066717 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[#, 2] &, 20000], 0}, 2]], 100] (* _Robert G. Wilson v_, Jul 21 2014 *)
%o A066717 (PARI) A066717(b=2,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 to get the c.f. of C[b] for other bases. - _M. F. Hasler_, Oct 25 2019
%Y A066717 Cf. A030190 & A066716 (binary & decimal digits of the binary Champernowne constant), A033307 (decimal Champernowne constant).
%Y A066717 Cf. A054635, A077771, A077772: base 3, decimals and continued fraction of ternary Champernowne constant.
%K A066717 base,cofr,nonn
%O A066717 0,3
%A A066717 _Robert G. Wilson v_, Jan 14 2002