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0, 1, 19, 271, 3439, 40951, 468559, 5217031, 56953279, 612579511, 6513215599, 68618940391, 717570463519, 7458134171671, 77123207545039, 794108867905351, 8146979811148159, 83322818300333431, 849905364703000879
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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.
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
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
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]
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REFERENCES
| G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 143
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..130
Alexander Bogomolny, Almost every integer has a digit 3 in it
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FORMULA
| G.f.: x/((1-9x)(1-10x)).
a(0) = 0, a(1) = 1, then a(n+1) = 9*a(n) + 10^n.
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]
E.g.f.: e^(10*x)-e^(9*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 14 2009]
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MATHEMATICA
| f[n_]:=10^n-9^n; f[Range[0, 40]] (*From Vladimir Joseph Stephan Orlovsky, Feb 14 2011*)
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PROG
| (MAGMA) [10^n - 9^n: n in [0..20]]; // Vincenzo Librandi, Apr 26 2011
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CROSSREFS
| Base 2: A000225, 3: A001047, 4: A005061, 5: A005060, 6: A005062, base 7: A016169, 8: A016177, 9: A016185 11: A016195 12: A016197.
Equals A155671 - 1.
Sequence in context: A142899 A083004 A139739 * A125476 A016248 A199819
Adjacent sequences: A016186 A016187 A016188 * A016190 A016191 A016192
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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