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

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

Offset

0,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

J. K. Sikora, The first 98093504 CFE coefficients of the binary Champernowne Constant (231 MB zipped)

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

Adjacent sequences: A066714 A066715 A066716 * A066718 A066719 A066720

Keyword

base,cofr,nonn

Author

Robert G. Wilson v, Jan 14 2002

Status

approved