|
|
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
|
|
|
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).
|
|
KEYWORD
|
base,cofr,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|