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

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

Offset

1,4

Links

Table of n, a(n) for n=1..12.

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

Formula

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

Prog

(Ruby) 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

Crossrefs

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

Cf. A143533 (another version of A038705).

Sequence in context: A178435 A183254 A390141 * A104729 A106661 A356768

Adjacent sequences: A143531 A143532 A143533 * A143535 A143536 A143537

Keyword

nonn,more,base

Author

Eric W. Weisstein, Aug 22 2008

Extensions

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

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

Status

approved