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

Author

John K. Sikora, Jun 27 2014

Keywords

• base
• nonn
• more

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)

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.)

Programs

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}

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.