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A124167 a(n) = 10*(10^n-1).

%I A124167 #23 Jan 27 2025 14:34:07
%S A124167 0,90,990,9990,99990,999990,9999990,99999990,999999990,9999999990,
%T A124167 99999999990,999999999990,9999999999990,99999999999990,
%U A124167 999999999999990,9999999999999990,99999999999999990,999999999999999990
%N A124167 a(n) = 10*(10^n-1).
%C A124167 a(n - 1) is the maximum difference between an n-digit number (written in base 10, nonzero leading digit) and the product of its digits. For n>1, it is also a number meeting that bound. See A070565. - _Devin Akman_, Apr 17 2019
%H A124167 Michael De Vlieger, <a href="/A124167/b124167.txt">Table of n, a(n) for n = 0..999</a>
%H A124167 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A124167 a(n) = 10*A002283(n).
%F A124167 From _G. C. Greubel_, Jun 30 2019: (Start)
%F A124167 a(n) = 90*A002275(n).
%F A124167 a(n) = 11*a(n-1) - 10*a(n-2).
%F A124167 G.f.: 10*(1/(1-10*x) - 1/(1-x)).
%F A124167 E.g.f.: 10*(exp(10*x) - exp(x)). (End)
%p A124167 a:=n->sum (10^(n-j+2)-10^(n-j+1),j=0..n): seq(a(n),n=0..20);
%t A124167 Array[10 (10^# - 1) &, 20, 0] (* _Michael De Vlieger_, Apr 21 2019 *)
%o A124167 (PARI) vector(20, n, n--; 10*(10^n -1)) \\ _G. C. Greubel_, Jun 30 2019
%o A124167 (Magma) [10*(10^n -1): n in [0..20]]; // _G. C. Greubel_, Jun 30 2019
%o A124167 (Sage) [10*(10^n -1) for n in (0..20)] # _G. C. Greubel_, Jun 30 2019
%o A124167 (GAP) List([0..20], n-> 10*(10^n -1)); # _G. C. Greubel_, Jun 30 2019
%Y A124167 Partial sums give 10*A099676.
%Y A124167 Cf. A002283, A002275, A070565.
%K A124167 easy,nonn
%O A124167 0,2
%A A124167 _Zerinvary Lajos_, Dec 02 2006