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A072290 Number of digits in the decimal expansion of the Champernowne constant that must be scanned to encounter all n-digit strings. 4
1, 11, 192, 2893, 38894, 488895, 5888896, 68888897, 788888898, 8888888899, 98888888900, 1088888888901, 11888888888902, 128888888888903, 1388888888888904, 14888888888888905, 158888888888888906, 1688888888888888907, 17888888888888888908, 188888888888888888909 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
"Decimal expansion of the Champernowne constant" excludes the initial 0 to the left of the decimal point.
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.
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
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+1) = n + A053541(n) - A002275(n) = n + A033713(n). - Lekraj Beedassy, Sep 16 2006
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
MAPLE
A072290:=n->10/9 - 10^n/9 + n + n*10^n: seq(A072290(n), n=0..30); # Wesley Ivan Hurt, Jul 06 2014
MATHEMATICA
f[n_] := 10/9 - 10^n/9 + n + n*10^n; Array[f, 20, 0] (* Robert G. Wilson v, Jul 06 2014 *)
PROG
(PARI) for(n=1, 23, print1(10^(n-1)*n+n-10^n/9+1/9" "));
(PARI) Vec((91*x^2-11*x+1)/((x-1)^2*(10*x-1)^2) + O(x^100)) \\ Colin Barker, May 22 2014
(Magma) [(10^(n-1)*n+n-10^n/9+1/9): n in [1..30]]; // Vincenzo Librandi, Jun 06 2011
CROSSREFS
Cf. A078427.
Sequence in context: A333759 A068649 A158509 * A258295 A213691 A112127
KEYWORD
nonn,base,easy
AUTHOR
Lekraj Beedassy, Jul 11 2002
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
STATUS
approved

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Last modified March 3 00:46 EST 2024. Contains 370499 sequences. (Running on oeis4.)