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A229127 Number of n-digit numbers containing the digit '0'. 2
1, 9, 171, 2439, 30951, 368559, 4217031, 46953279, 512579511, 5513215599, 58618940391, 617570463519, 6458134171671, 67123207545039, 694108867905351, 7146979811148159, 73322818300333431, 749905364703000879, 7649148282327007911, 77842334540943071199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Other than the number 0 itself, numbers with leading zeros are not allowed, so the general formula is a(n)=9*10^(n-1)-9^n, which is simply the number of n-digit numbers that begin with a nonzero digit (9*10^(n-1)) minus the number of n-digit numbers consisting only of nonzero digits (9^n). (Because of the 1-digit number 0 itself, the general formula does not apply at n=1.)

Other than the number 1, and 9 which is a semiprime, the minimum number of possible prime factors with multiplicity of a(n) = 3, which holds for 171 = 3^2 * 19; 2439 = 3^2 * 271; 46953279 = 3^2 * 5217031; 617570463519 = 3^2 * 68618940391; 77842334540943071199 = 3^2 * 8649148282327007911. - Jonathan Vos Post, Sep 16 2013

LINKS

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (19,-90).

FORMULA

For n>1, a(n)=9*10^(n-1)-9^n.

For n>2, a(n)=9*(a(n-1)+10^(n-2)).

G.f.: x*(1-10*x+90*x^2)/((1-9*x)*(1-10*x)). - R. J. Mathar, Sep 14 2013

a(n) = A217094(n) - A217094(n-1), for n>1. - Hieronymus Fischer, Dec 27 2013

EXAMPLE

a(2) = 9, since there are 9 2-digit numbers that contain a '0'.

CROSSREFS

Cf. A011540, A050720, A217094.

Sequence in context: A121477 A055407 A083155 * A132897 A238466 A049212

Adjacent sequences:  A229124 A229125 A229126 * A229128 A229129 A229130

KEYWORD

nonn,base,easy

AUTHOR

Jon E. Schoenfield, Sep 14 2013

EXTENSIONS

Example added and g.f. corrected by Hieronymus Fischer, Dec 27 2013

STATUS

approved

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Last modified September 20 04:16 EDT 2021. Contains 347577 sequences. (Running on oeis4.)