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%I #24 Sep 08 2022 08:45:49
%S 2,3,5,7,13,14,16,18,24,25,27,29,35,36,38,40,46,47,49,51,57,58,60,62,
%T 68,69,71,73,79,80,82,84,90,91,93,95,101,102,104,106,112,113,115,117,
%U 123,124,126,128,134,135,137,139,145,146,148,150,156,157,159,161,167,168
%N Numbers that are congruent to {2, 3, 5, 7} mod 11.
%H Vincenzo Librandi, <a href="/A168484/b168484.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F From _R. J. Mathar_, Mar 21 2010: (Start)
%F G.f.: x*(2 + x + 2*x^2 + 2*x^3 + 4*x^4)/ ((1+x)*(x^2+1)*(x-1)^2).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. (End)
%F a(n) = (22*n - 21 - 5*i^(2*n) - (3-5*i)*i^(-n) - (3+5*i)*i^n)/8 where i = sqrt(-1). - _Wesley Ivan Hurt_, Jun 07 2016
%F E.g.f.: (1/4)*(16 + (11*x -13)*cosh(x) + (11*x - 8)*sinh(x) - 3*cos(x) + 5*sin(x)). - _G. C. Greubel_, Jul 23 2016
%p A168484:=n->(22*n-21-5*I^(2*n)-(3-5*I)*I^(-n)-(3+5*I)*I^n)/8: seq(A168484(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t CoefficientList[Series[(2 + x + 2 x^2 + 2 x^3 + 4 x^4)/((1 + x) (x^2+1) (x-1)^2), {x, 0, 100}], x] (* _Vincenzo Librandi_, Sep 24 2014 *)
%t Select[Range[168], MemberQ[{2,3,5,7}, Mod[#,11]]&] (* _Ray Chandler_, Jul 07 2015 *)
%t LinearRecurrence[{1,0,0,1,-1}, {2,3,5,7,13}, 62] (* _Ray Chandler_, Jul 07 2015 *)
%o (Magma) [n : n in [0..200] | n mod 11 in [2, 3, 5, 7]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 28 2009
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