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A198971 a(n) = 5*10^n - 1.

%I A198971 #46 May 02 2025 16:04:41
%S A198971 4,49,499,4999,49999,499999,4999999,49999999,499999999,4999999999,
%T A198971 49999999999,499999999999,4999999999999,49999999999999,
%U A198971 499999999999999,4999999999999999,49999999999999999,499999999999999999,4999999999999999999,49999999999999999999,499999999999999999999
%N A198971 a(n) = 5*10^n - 1.
%C A198971 Also maximal value of GCD of 2 distinct (n+1)-digit numbers (compare with A126687). - _Michel Marcus_, Jun 24 2013
%C A198971 Also, a(n) is the largest obtained remainder when an (n+1)-digit number m is divided by any k with 1 <= k <= m. This remainder is obtained when 10^(n+1)-1 is divided by 5*10^n, example: 999 = 500 * 1 + 499, and a(2) = 499. - _Bernard Schott_, Nov 23 2021
%C A198971 Also numbers k whose digital reversal equals 2*(k - 2). - _Stefano Spezia_, Sep 15 2024
%H A198971 Vincenzo Librandi, <a href="/A198971/b198971.txt">Table of n, a(n) for n = 0..200</a>
%H A198971 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A198971 a(n) = 10*a(n-1) + 9.
%F A198971 a(n) = 11*a(n-1) - 10*a(n-2), n>1.
%F A198971 G.f.: (4 + 5*x)/(1 - 11*x + 10*x^2). - _Vincenzo Librandi_, Jan 03 2013
%F A198971 E.g.f.: exp(x)*(5*exp(9*x) - 1). - _Stefano Spezia_, Nov 17 2022
%F A198971 a(n) = A086942(n+1)/8 = A086940(n+1)/4 = A099150(n+1)/2. - _Elmo R. Oliveira_, May 02 2025
%t A198971 CoefficientList[Series[(4 + 5*x)/(1 - 11*x + 10*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 03 2013 *)
%t A198971 LinearRecurrence[{11,-10},{4,49},20] (* _Harvey P. Dale_, Dec 30 2018 *)
%o A198971 (Magma) [5*10^n-1 : n in [0..20]];
%o A198971 (PARI) a(n)=5*10^n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A198971 Cf. A002283, A086940, A086942, A099150, A126687.
%K A198971 nonn,easy
%O A198971 0,1
%A A198971 _Vincenzo Librandi_, Nov 02 2011