A077772 Continued fraction expansion of the ternary Champernowne constant.

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, 2, 1, 3, 1, 10, 1, 21, 1, 1, 4, 3, 577, 1, 1079268324684171943515797470873767312825026176345571319042096689270, 1, 1, 1, 3, 4, 21, 3, 1, 9, 1

Offset

0,4

Links

John K. Sikora, Table of n, a(n) for n = 0..2061 (terms n = 0..1155 from Robert G. Wilson v)

J. K. Sikora, The first 2982556 terms of the CFE of the ternary Champernowne Constant (141 MB zipped)

Eric Weisstein's World of Mathematics, Ternary Champernowne Constant

Mathematica

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 *)

Prog

(PARI) \p 10000
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
(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

Crossrefs

Cf. A054635 (ternary digits), A077771 (decimals).

Cf. A030190, A066716, A066717: binary digits, decimals and continued fraction of the binary Champernowne constant; A033307: decimal Champernowne constant.

Sequence in context: A358972 A073581 A078081 * A083150 A066146 A258035

Adjacent sequences: A077769 A077770 A077771 * A077773 A077774 A077775

Keyword

nonn,base,cofr

Author

Eric W. Weisstein, Nov 15 2002

Status

approved