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A066717 The continued fraction for the "binary" Champernowne constant. 8
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Eric E. Weisstein, Binary Champernowne Constant
MATHEMATICA
a = {}; Do[a = Append[a, IntegerDigits[n, 2]], {n, 1, 10^3} ]; ContinuedFraction[ N[ FromDigits[ {Flatten[a], 0}, 2], 500]]
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 *)
PROG
(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
CROSSREFS
Cf. A030190 & A066716 (binary & decimal digits of the binary Champernowne constant), A033307 (decimal Champernowne constant).
Cf. A054635, A077771, A077772: base 3, decimals and continued fraction of ternary Champernowne constant.
Sequence in context: A085580 A092151 A365477 * A176395 A309646 A195494
KEYWORD
base,cofr,nonn
AUTHOR
Robert G. Wilson v, Jan 14 2002
STATUS
approved

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Last modified July 22 18:05 EDT 2024. Contains 374540 sequences. (Running on oeis4.)