A244333 Number of ternary digits in the high-water marks of the terms of the continued fraction of the base 3 Champernowne constant (A077772).

0, 1, 1, 4, 5, 33, 139, 515, 1809, 6181, 20759, 68871, 226333, 738089, 2391459, 7705867, 24711977, 78918957, 251105839

Offset

1,4

Links

John K. Sikora, Table of n, a(n) for n = 1..19

J. K. Sikora, Analysis of the High Water Mark Convergents of Champernowne's Constant in Various Bases, arXiv:1408.0261 [math.NT]

J. K. Sikora, Number of ternary digits of the first 2982556 terms of the continued fraction of the base 3 Champernowne Constant (7 MB zipped)

Formula

It appears that: Define NCD(N)=3-N+(sum{m=1..(N-3)} 2*m*3^(m-1)); then for n>=5, a(n) = NCD(n)-2*NCD(n-1)-3*(n-2)+4.

Prog

(Ruby) puts (5..19).collect {|n| (1..(n-3)).inject(0) {|sum, m| sum+2*m*3**(m-1)}+3-n-2*((1..(n-4)).inject(0) {|sum1, m1| sum1+2*m1*3**(m1-1)}+3-(n-1))-3*(n-2)+4}

Crossrefs

Cf. A077772 (Continued fraction expansion of the ternary Champernowne constant.)

Cf. A244757 (Incrementally largest terms in the continued fraction for the base 3 Champernowne constant.)

Cf. A244332 (Position of the incrementally largest term in the continued fraction for the base 3 Champernowne constant.)

Sequence in context: A262711 A215614 A013468 * A041907 A228662 A151450

Adjacent sequences: A244330 A244331 A244332 * A244334 A244335 A244336

Keyword

base,nonn,more

Author

John K. Sikora, Jun 27 2014

Status

approved