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%I #14 Jun 29 2023 18:08:00
%S 4,9,55,111,1111,11111,111111,1111111,11111111,111111111,1111111111,
%T 11111111111,111111111111,1111111111111,11111111111111,
%U 111111111111111,1111111111111111,11111111111111111,111111111111111111
%N a(1) = 4; a(n) = smallest palindromic number of the form k*a(n-1) + 1 with k > 1.
%H Vincenzo Librandi, <a href="/A069507/b069507.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11, -10).
%F a(n) = {10^(n-1)-1}/9 for n > 3.
%F From _Chai Wah Wu_, Jun 20 2016: (Start)
%F a(n) = 11*a(n-1) - 10*a(n-2) for n > 4.
%F G.f.: (440*x^4 - 404*x^3 - 4*x^2 - 35*x + 4)/((x - 1)*(10*x - 1)). (End)
%t CoefficientList[Series[(440 x^4 - 404 x^3 - 4 x^2 - 35 x + 4) / ((x - 1) (10 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jun 21 2016 *)
%o (Magma) I:=[4,9,55,111,1111]; [n le 5 select I[n] else 11*Self(n-1)-10*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Jun 21 2016
%Y Cf. A069505, A069506, A069508, A069509, A069510.
%K nonn,base
%O 0,1
%A _Amarnath Murthy_, Mar 30 2002
%E More terms from _Patrick De Geest_, Jun 11 2003
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