A038705 -id:A038705 - cp's OEIS frontend

A143533 a(n) = A038705(n) - 1.

0, 1, 2, 4, 18, 40, 162, 526, 1708, 4838, 13522, 34062

Offset: 1

Eric W. Weisstein, Aug 22 2008

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], 2012.
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

Another version of A038705.
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.).

Added a(10) (from Mark Sofroniou), Eric W. Weisstein, Sep 04 2008
Edited by N. J. A. Sloane, Apr 03 2010 to reflect the fact that A038705 is the primary version of this sequence
a(12) from John K. Sikora, Aug 24 2012

A038706 Position of the first occurrence of n in continued fraction for Champernowne constant (A030167).

Original entry on oeis.org

4, 28, 13, 9, 93, 20, 31, 2, 3, 339, 71, 126, 107, 48, 18, 292, 327, 133, 611, 342, 23, 202, 441, 164, 512, 235, 957, 349, 528, 77, 179, 591, 307, 381, 2011, 245, 2435, 187, 1870, 117, 1359, 1071, 762, 4199, 4309, 2308, 4294, 1012, 1501, 3490, 2249, 283

Offset: 1

Hans Havermann, May 01 2000

Only 187 terms of the sequence are known. The position of 188 is > 82328. - Eric W. Weisstein, Jun 29 2013

John K. Sikora and Eric W. Weisstein, Table of n, a(n) for n = 1..187 (terms n = 1..112 from John K. Sikora)

Cf. A030167, A038704, A038705.

A038704 Incrementally largest term in continued fraction for Champernowne constant (A030167).

Original entry on oeis.org

8, 9, 149083

Offset: 1

Hans Havermann, May 01 2000

The next term (a(4)) has 166 digits; a(5) has 2504 digits. - Harvey P. Dale, Sep 18 2016

H. Havermann, Number of Digits in Some Champernowne-Continued-Fraction Terms

Cf. A030167, A038705, A038706.

DeleteDuplicates[Block[{$MaxExtraPrecision=10000},ContinuedFraction[ ChampernowneNumber[],50]],GreaterEqual] (* Harvey P. Dale, Apr 02 2023 *)

The next term has 166 digits.

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

A143533 a(n) = A038705(n) - 1.

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A038706 Position of the first occurrence of n in continued fraction for Champernowne constant (A030167).

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A038704 Incrementally largest term in continued fraction for Champernowne constant (A030167).

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

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