This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016189 #53 Sep 08 2022 08:44:40
%S A016189 0,1,19,271,3439,40951,468559,5217031,56953279,612579511,6513215599,
%T A016189 68618940391,717570463519,7458134171671,77123207545039,
%U A016189 794108867905351,8146979811148159,83322818300333431,849905364703000879,8649148282327007911,87842334540943071199,890581010868487640791
%N A016189 a(n) = 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_, 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 0.2} (1-0.5*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. - _R. J. Mathar_, Nov 27 2008
%C A016189 First differences are given in A088924. - _M. F. Hasler_, May 04 2015
%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 Vincenzo Librandi, <a href="/A016189/b016189.txt">Table of n, a(n) for n = 0..130</a>
%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>
%H A016189 John Elias, <a href="/A016189/a016189.png">Illustration of Initial Terms</a>
%H A016189 James Grime, <a href="https://www.youtube.com/watch?v=UfEiJJGv4CE">3 is everywhere</a>, Numberphile video
%H A016189 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (19, -90).
%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. - _Philippe Deléham_, Jan 01 2009
%F A016189 E.g.f.: e^(10*x) - e^(9*x). - _Mohammad K. Azarian_, Jan 14 2009
%t A016189 f[n_]:=10^n-9^n;f[Range[0,40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2011 *)
%o A016189 (Magma) [10^n - 9^n: n in [0..20]]; // _Vincenzo Librandi_, Apr 26 2011
%o A016189 (Haskell)
%o A016189 a016189 n = 10 ^ n - 9 ^ n
%o A016189 a016189_list = 0 : zipWith (+) (map (* 9) a016189_list) a011557_list
%o A016189 -- _Reinhard Zumkeller_, Apr 03 2015
%o A016189 (PARI) a(n)=10^n-9^n \\ _M. F. Hasler_, May 04 2015
%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 Cf. A011557, A011533.
%K A016189 nonn,easy
%O A016189 0,3
%A A016189 _N. J. A. Sloane_