cp's OEIS Frontend

A072290 Number of digits in the decimal expansion of the Champernowne constant that must be scanned to encounter all n-digit strings.

%I A072290 #42 Feb 16 2025 08:32:46
%S A072290 1,11,192,2893,38894,488895,5888896,68888897,788888898,8888888899,
%T A072290 98888888900,1088888888901,11888888888902,128888888888903,
%U A072290 1388888888888904,14888888888888905,158888888888888906,1688888888888888907,17888888888888888908,188888888888888888909
%N A072290 Number of digits in the decimal expansion of the Champernowne constant that must be scanned to encounter all n-digit strings.
%C A072290 "Decimal expansion of the Champernowne constant" excludes the initial 0 to the left of the decimal point.
%C A072290 In writing out all numbers 1 through 10^n inclusive, exactly a(n) digits are used, of which a(n-1) are 0's and there are n*10^(n-1) of each of the other digits, with still an extra one for 1's.
%D A072290 J. D. E. Konhauser et al.  "Digit Counting." Problem 134 in Which Way Did The Bicycle Go?  Dolciani Math. Exp. No. 18.  Washington, DC: Math. Assoc. Amer., pp. 40 and 173-174, 1996.
%H A072290 Eric W. Weisstein, <a href="/A072290/b072290.txt">Table of n, a(n) for n = 0..1000</a> [replacing an earlier file from Vincenzo Librandi]
%H A072290 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChampernowneConstantDigits.html">Champernowne Constant Digits</a>
%H A072290 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConstantDigitScanning.html">Constant Digit Scanning</a>
%H A072290 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-141,220,-100).
%F A072290 a(n) = 10/9 - 10^n/9 + n + n*10^n.
%F A072290 a(n+1) = a(n) + 9*(n+1)*10^n + 1.
%F A072290 a(n+1) = n + A053541(n) - A002275(n) = n + A033713(n). - _Lekraj Beedassy_, Sep 16 2006
%F A072290 a(n) = 22*a(n-1) - 141*a(n-2) + 220*a(n-3) - 100*a(n-4). - _Colin Barker_, May 22 2014
%F A072290 G.f.: (91*x^2-11*x+1) / ((x-1)^2*(10*x-1)^2). - _Colin Barker_, May 22 2014
%p A072290 A072290:=n->10/9 - 10^n/9 + n + n*10^n: seq(A072290(n), n=0..30); # _Wesley Ivan Hurt_, Jul 06 2014
%t A072290 f[n_] := 10/9 - 10^n/9 + n + n*10^n; Array[f, 20, 0] (* _Robert G. Wilson v_, Jul 06 2014 *)
%o A072290 (PARI) for(n=1,23,print1(10^(n-1)*n+n-10^n/9+1/9" "));
%o A072290 (PARI) Vec((91*x^2-11*x+1)/((x-1)^2*(10*x-1)^2) + O(x^100)) \\ _Colin Barker_, May 22 2014
%o A072290 (Magma) [(10^(n-1)*n+n-10^n/9+1/9): n in [1..30]]; // _Vincenzo Librandi_, Jun 06 2011
%Y A072290 Cf. A078427.
%K A072290 nonn,base,easy
%O A072290 0,2
%A A072290 _Lekraj Beedassy_, Jul 11 2002
%E A072290 More terms from _Jason Earls_, Dec 18 2002
%E A072290 Description rewritten by _Eric W. Weisstein_, Sep 14 2013
%E A072290 More terms from _Colin Barker_, May 22 2014