A244757 -id:A244757 - cp's OEIS frontend

A244332 Position of the incrementally largest term in the continued fraction for the base 3 Champernowne constant (A077772).

1, 2, 4, 5, 7, 19, 39, 121, 321, 813, 2063, 4957, 11731, 26329, 59501, 132273, 294475, 644557, 1392933, 2982557

Offset: 1

John K. Sikora, Jun 26 2014

John K. Sikora, Table of n, a(n) for n = 1..20
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)

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

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

Original entry on oeis.org

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

Offset: 1

John K. Sikora, Jun 27 2014

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)

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.)

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}

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.

cp's OEIS Frontend

A244332 Position of the incrementally largest term in the continued fraction for the base 3 Champernowne constant (A077772).

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

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