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A047318 Numbers that are congruent to {0, 1, 2, 4, 5, 6} mod 7.

%I A047318 #30 Jul 02 2025 16:01:57
%S A047318 0,1,2,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,22,23,25,26,27,28,29,
%T A047318 30,32,33,34,35,36,37,39,40,41,42,43,44,46,47,48,49,50,51,53,54,55,56,
%U A047318 57,58,60,61,62,63,64,65,67,68,69,70,71,72,74,75,76,77,78,79,81,82,83
%N A047318 Numbers that are congruent to {0, 1, 2, 4, 5, 6} mod 7.
%C A047318 Complement of A017017. - _Michel Marcus_, Sep 10 2015
%H A047318 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A047318 G.f.: x^2*(1+x+2*x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 03 2011
%F A047318 From _Wesley Ivan Hurt_, Sep 10 2015: (Start)
%F A047318 a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F A047318 a(n) = n + floor((n-4)/6). (End)
%F A047318 From _Wesley Ivan Hurt_, Jun 15 2016: (Start)
%F A047318 a(n) = (42*n-39+3*cos(n*Pi)-4*sqrt(3)*cos((1+4*n)*Pi/6)+12*sin((1-2*n)*Pi/6))/36.
%F A047318 a(6k) = 7k-1, a(6k-1) = 7k-2, a(6k-2) = 7k-3, a(6k-3) = 7k-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)
%p A047318 for n from 0 to 200 do if n mod 7 <> 3 then printf(`%d,`,n) fi: od:
%p A047318 A047318:=n->n+floor((n-4)/6): seq(A047318(n), n=1..100); # _Wesley Ivan Hurt_, Sep 10 2015
%t A047318 Table[n+Floor[(n-4)/6], {n,100}] (* _Wesley Ivan Hurt_, Sep 10 2015 *)
%t A047318 LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7}, 100] (* _Vincenzo Librandi_, Sep 11 2015 *)
%t A047318 DeleteCases[Range[0,100],_?(Mod[#,7]==3&)] (* _Harvey P. Dale_, May 07 2016 *)
%o A047318 (Magma) [n+Floor((n-4)/6) : n in [1..100]]; // _Wesley Ivan Hurt_, Sep 10 2015
%o A047318 (Magma) [n : n in [0..140] | n mod 7 in [0, 1, 2, 4, 5, 6]]; // _Vincenzo Librandi_, Sep 11 2015
%Y A047318 Cf. A017017.
%K A047318 nonn,easy
%O A047318 1,3
%A A047318 _N. J. A. Sloane_
%E A047318 More terms from _James Sellers_, Feb 19 2001