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%I #31 Feb 13 2015 02:10:55
%S 0,1,1,6,166,2504,33102,411100,4911098,57111096,651111094,7311111092
%N Number of decimal digits in the high-water marks of the terms of the continued fraction of the (base-10) Champernowne constant.
%H J. K. Sikora, <a href="http://arxiv.org/abs/1210.1263">On the High Water Mark Convergents of Champernowne's Constant in Base Ten</a>, arXiv:1210.1263 [math.NT]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChampernowneConstantContinuedFraction.html">Champernowne Constant Continued Fraction</a>
%F 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
%o (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
%Y Cf. A038705 (position of the incrementally largest term in continued fraction for Champernowne constant).
%Y Cf. A143533 (another version of A038705).
%K nonn,more,base
%O 1,4
%A _Eric W. Weisstein_, Aug 22 2008
%E a(11) = 651111094 (from Mark Sofroniou), _Eric W. Weisstein_, Sep 04 2008
%E a(12) = 7311111092 from _Eric W. Weisstein_, Jun 29 2013
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