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A033714 Number of zeros in numbers 0 to 999..9 (n digits). 3
1, 10, 190, 2890, 38890, 488890, 5888890, 68888890, 788888890, 8888888890, 98888888890, 1088888888890, 11888888888890, 128888888888890, 1388888888888890, 14888888888888890, 158888888888888890, 1688888888888888890, 17888888888888888890, 188888888888888888890 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence also gives the total count of digits of n below 10^n. In such counts it makes sense to omit 10^0 as we are interested in having ten digits under each power of 10. For each power of 10 the total number of digits 0-9 is always the total of zeros for the next power. For example, at 10^1 there is 1 of each numeral 0-9, total 10 digits. At 10^2, the number of zeros is 10, with 20 each for the other 9 numerals and so on. - Enoch Haga, May 13 2006

Also the position of 10^n in Champernowne's constant (A033307). See Sikora, p. 3. - Robert G. Wilson v, Jun 29 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

John K. Sikora, On the High Water Mark Convergents of Champernowne's Constant in Base Ten, arXiv:1210.1263 [math.NT], 2012.

Index entries for linear recurrences with constant coefficients, signature (21,-120,100).

FORMULA

a(n) = 10^(n-1)*n-(1/9)*10^n+10/9. - Robert Israel, Jun 30 2014

G.f.: -x*(100*x^2-11*x+1) / ((x-1)*(10*x-1)^2). - Colin Barker, Jan 27 2015

MATHEMATICA

a[1] = 1; a[n_] := a[n] = 9*10^(n-2)*(n-1) + a[n-1]; Table[a[n], {n, 1, 17}] (* Jean-Fran├žois Alcover, Jul 13 2012 *)

f[n_] := 1 + Sum[9 m*10^(m - 1), {m, n}]; Array[f, 18, 0] (* Robert G. Wilson v, Jun 29 2014 *)

PROG

(MAGMA) [(9*n*10^n-10*10^n+100)/90: n in [1..20]]: // Vincenzo Librandi, Jul 01 2014

(PARI) Vec(-x*(100*x^2-11*x+1)/((x-1)*(10*x-1)^2)  + O(x^100)) \\ Colin Barker, Jan 27 2015

CROSSREFS

Cf. A033713.

Sequence in context: A173813 A249643 A056174 * A169959 A131521 A113373

Adjacent sequences:  A033711 A033712 A033713 * A033715 A033716 A033717

KEYWORD

nonn,base,nice,easy

AUTHOR

Olivier Gorin (gorin(AT)roazhon.inra.fr)

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

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Last modified April 1 04:15 EDT 2020. Contains 333155 sequences. (Running on oeis4.)