0,3

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]

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 143

Alexander Bogomolny, Almost every integer has a digit 3 in it

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]

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 this_sequence A125476 A016248 A016187

Adjacent sequences: A016186 A016187 A016188 this_sequence A016190 A016191 A016192

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).