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%I #23 Sep 08 2022 08:44:56
%S 2,3,5,8,9,11,14,15,17,20,21,23,26,27,29,32,33,35,38,39,41,44,45,47,
%T 50,51,53,56,57,59,62,63,65,68,69,71,74,75,77,80,81,83,86,87,89,92,93,
%U 95,98,99,101,104,105,107,110,111,113,116,117,119,122,123,125,128,129
%N Numbers that are congruent to {2, 3, 5} mod 6.
%C For n>0: a(n) = greatest m<=2*(n+1) coprime to a(n-1). - _Reinhard Zumkeller_, Oct 31 2005
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F G.f.: x*(x+2)*(1+x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (6*n-2-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3.
%F a(3k) = 6k-1, a(3k-1) = 6k-3, a(3k-2) = 6k-4. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (3+2*sqrt(3))*Pi/36 - log(2+sqrt(3))/(2*sqrt(3)) + log(2)/6. - _Amiram Eldar_, Dec 16 2021
%p A047254:=n->(6*n-2-cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/3: seq(A047254(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t Select[Range[0, 150], MemberQ[{2, 3, 5}, Mod[#, 6]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)
%o (Magma) [n: n in [0..150] | n mod 6 in {2, 3, 5} ]; // _Vincenzo Librandi_, Dec 25 2010
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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