A072290 Number of digits in the decimal expansion of the Champernowne constant that must be scanned to encounter all n-digit strings.
1, 11, 192, 2893, 38894, 488895, 5888896, 68888897, 788888898, 8888888899, 98888888900, 1088888888901, 11888888888902, 128888888888903, 1388888888888904, 14888888888888905, 158888888888888906, 1688888888888888907, 17888888888888888908, 188888888888888888909
Offset: 0
References
- 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.
Links
- Eric W. Weisstein, Table of n, a(n) for n = 0..1000 [replacing an earlier file from Vincenzo Librandi]
- Eric Weisstein's World of Mathematics, Champernowne Constant Digits
- Eric Weisstein's World of Mathematics, Constant Digit Scanning
- Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100).
Crossrefs
Cf. A078427.
Programs
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Magma
[(10^(n-1)*n+n-10^n/9+1/9): n in [1..30]]; // Vincenzo Librandi, Jun 06 2011
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Maple
A072290:=n->10/9 - 10^n/9 + n + n*10^n: seq(A072290(n), n=0..30); # Wesley Ivan Hurt, Jul 06 2014
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Mathematica
f[n_] := 10/9 - 10^n/9 + n + n*10^n; Array[f, 20, 0] (* Robert G. Wilson v, Jul 06 2014 *)
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PARI
for(n=1,23,print1(10^(n-1)*n+n-10^n/9+1/9" "));
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PARI
Vec((91*x^2-11*x+1)/((x-1)^2*(10*x-1)^2) + O(x^100)) \\ Colin Barker, May 22 2014
Formula
a(n) = 10/9 - 10^n/9 + n + n*10^n.
a(n+1) = a(n) + 9*(n+1)*10^n + 1.
a(n) = 22*a(n-1) - 141*a(n-2) + 220*a(n-3) - 100*a(n-4). - Colin Barker, May 22 2014
G.f.: (91*x^2-11*x+1) / ((x-1)^2*(10*x-1)^2). - Colin Barker, May 22 2014
Extensions
More terms from Jason Earls, Dec 18 2002
Description rewritten by Eric W. Weisstein, Sep 14 2013
More terms from Colin Barker, May 22 2014
Comments