Search: id:A016189
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%I A016189
%S A016189 0,1,19,271,3439,40951,468559,5217031,56953279,612579511,
%T A016189 6513215599,68618940391,717570463519,7458134171671,77123207545039,
%U A016189 794108867905351,8146979811148159,83322818300333431,849905364703000879
%N A016189 10^n - 9^n.
%C A016189 Almost all numbers contain any given sequence of digits (in any base) 
               [Theorem 143 of Hardy and Wright]. a(7) = 5217031, more than 52% 
               of the numbers < 10^7 contain any given nonzero decimal digit. - 
               Frank.Ellermann(AT)t-online.de, May 30, 2001.
%C A016189 a(n) gives the number of integers from 0 to 10^n-1 which contain (at 
               least) any one given decimal digit except 0. - Michael Taktikos, 
               Aug 24 2004
%C A016189 These are the numerators of a(n)=(integral{x=0 to .2} (1-.5*x)^n dx). 
               E.g. a(3)=3439/20000. The denominators are b(n)=5*(n+1)*10^n. E.g. 
               b(3)=20000. - Al Hakanson (hawkuu(AT)excite.com), Feb 22 2004
%C A016189 Binomial transforms of sequences defined by a(n)=(C+1)^n-C^n are the 
               sequences (C+2)^n-(C+1)^n. The binomial transform of this here is 
               in A016195, for example. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 27 2008]
%D A016189 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, th. 143
%H A016189 Alexander Bogomolny, <a href="http://www.cut-the-knot.org/do_you_know/
               digit3.shtml">Almost every integer has a digit 3 in it</a>
%F A016189 G.f.: x/((1-9x)(1-10x)).
%F A016189 a(0) = 0, a(1) = 1, then a(n+1) = 9*a(n) + 10^n.
%F A016189 a(n)=19*a(n-1)-90*a(n-2), n>1 ; a(0)=0, a(1)=1 . [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Jan 01 2009]
%F A016189 E.g.f.: e^(10*x)-e^(9*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Jan 14 2009]
%Y A016189 Base 2: A000225, 3: A001047, 4: A005061, 5: A005060, 6: A005062, base 
               7: A016169, 8: A016177, 9: A016185 11: A016195 12: A016197.
%Y A016189 Equals A155671 - 1.
%Y A016189 Sequence in context: A142899 A083004 A139739 this_sequence A125476 A016248 
               A016187
%Y A016189 Adjacent sequences: A016186 A016187 A016188 this_sequence A016190 A016191 
               A016192
%K A016189 nonn,easy
%O A016189 0,3
%A A016189 N. J. A. Sloane (njas(AT)research.att.com).

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