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%I #23 Sep 08 2022 08:45:50
%S 1,51,551,5551,55551,555551,5555551,55555551,555555551,5555555551,
%T 55555555551,555555555551,5555555555551,55555555555551,
%U 555555555555551,5555555555555551,55555555555555551,555555555555555551
%N a(n) = (5*10^n - 41)/9 for n > 0.
%C Primes up to n=100 are 555555555551 and 5555555555551; the next prime term has 609 digits (see A056684).
%H Vincenzo Librandi, <a href="/A173804/b173804.txt">Table of n, a(n) for n = 1..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F a(n) = 10*a(n-1) + 41 with a(0)=-4.
%F G.f.: x*(1+40*x)/((1-x)*(1-10*x)). - _Vincenzo Librandi_, Jul 05 2012
%F a(n) = 11*a(n-1) - 10*a(n-2). - _Vincenzo Librandi_, Jul 05 2012
%t CoefficientList[Series[(1+40*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* _Vincenzo Librandi_, Jul 05 2012 *)
%t Table[FromDigits[PadLeft[{1},n,5]],{n,20}] (* or *) LinearRecurrence[ {11,-10},{1,51},20](* _Harvey P. Dale_, Dec 04 2021 *)
%o (Magma)[(5*10^n-41)/9: n in [1..20]]; // _Vincenzo Librandi_, Jul 05 2012
%Y Cf. A056684 (numbers n such that (5*10^(n+1)-41)/9 is prime). - _Klaus Brockhaus_, Feb 28 2010
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, Feb 25 2010
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