A143533 -id:A143533 - cp's OEIS frontend

A038705 Position of the incrementally largest term in continued fraction for Champernowne constant (A030167).

1, 2, 3, 5, 19, 41, 163, 527, 1709, 4839, 13523, 34063

Offset: 1

Hans Havermann, May 01 2000

H. Havermann, Number of Digits in Some Champernowne-Continued-Fraction Terms
J. K. Sikora, Number of Digits in the CFE of Champernowne's Constant to the Coefficient Before HWM #12
J. K. Sikora, On the High Water Mark Convergents of Champernowne's Constant in Base Ten, arXiv:1210.1263 [math.NT]
J. K. Sikora, Champernowne's Constant CFE Coefficients to HWM #12 (789 MB unzipped)
J. K. Sikora, Champernowne's Constant CFE Calculation Program Source
Eric Weisstein's World of Mathematics, Champernowne Constant Continued Fraction

Cf. A030167, A038704, A038706.
See A143533 for another version.
Cf. A143532 (number of decimal digits in n-th term of c.f.).
Cf. A143534 (number of decimal digits in a(n)-th term of c.f.).

a(10) = 13523 (from Mark Sofroniou) contributed by Eric W. Weisstein, Sep 04 2008.
Edited by N. J. A. Sloane, Apr 03 2010.
a(11) = 34063 contributed by John K. Sikora, Aug 24 2012.

A143534 Number of decimal digits in the high-water marks of the terms of the continued fraction of the (base-10) Champernowne constant.

Original entry on oeis.org

0, 1, 1, 6, 166, 2504, 33102, 411100, 4911098, 57111096, 651111094, 7311111092

Offset: 1

Eric W. Weisstein, Aug 22 2008

J. K. Sikora, On the High Water Mark Convergents of Champernowne's Constant in Base Ten, arXiv:1210.1263 [math.NT]
Eric Weisstein's World of Mathematics, Champernowne Constant Continued Fraction

Cf. A038705 (position of the incrementally largest term in continued fraction for Champernowne constant).

Cf. A143533 (another version of A038705).

puts (4..13).collect {|n| (1..(n-3)).inject(0) {|sum, m| sum+9*m*10**(m-1)}+3-n-2*((1..(n-4)).inject(0) {|sum1, m1| sum1+9*m1*10**(m1-1)}+3-(n-1))-3*(n-2)+4} # John K. Sikora, Aug 25 2012

It appears that: For N>=3, define NCD(N)=3-N+(sum{m=1..(N-3), m>0} 9*m*10^(m-1)); then for n>=4, a(n) = NCD(n) - 2*NCD(n-1) - 3*(n-2) + 4. - John K. Sikora, Aug 25 2012

a(11) = 651111094 (from Mark Sofroniou), Eric W. Weisstein, Sep 04 2008

a(12) = 7311111092 from Eric W. Weisstein, Jun 29 2013

cp's OEIS Frontend

A038705 Position of the incrementally largest term in continued fraction for Champernowne constant (A030167).

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