cp's OEIS Frontend

A047310 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7.

%I A047310 #29 Dec 02 2024 15:48:19
%S A047310 0,1,3,4,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,24,25,26,27,28,
%T A047310 29,31,32,33,34,35,36,38,39,40,41,42,43,45,46,47,48,49,50,52,53,54,55,
%U A047310 56,57,59,60,61,62,63,64,66,67,68,69,70,71,73,74,75,76,77,78
%N A047310 Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7.
%C A047310 Complement of A017005. - _Michel Marcus_, Sep 08 2015
%H A047310 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1)
%F A047310 G.f.: x^2*(1+2*x+x^2+x^3+x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F A047310 From _Wesley Ivan Hurt_, Sep 08 2015: (Start)
%F A047310 a(n) = a(n-1)+a(n-6)-a(n-7) for n>7.
%F A047310 a(n) = n + floor((n-3)/6). (End)
%F A047310 From _Wesley Ivan Hurt_, Jun 15 2016: (Start)
%F A047310 a(n) = (42*n-33-3*cos(n*Pi)+4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/36.
%F A047310 a(6k) = 7k-1, a(6k-1) = 7k-2, a(6k-2) = 7k-3, a(6k-3) = 7k-4, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)
%p A047310 A047310:=n->n+floor((n-3)/6): seq(A047310(n), n=1..100); # _Wesley Ivan Hurt_, Sep 08 2015
%t A047310 Table[n+Floor[(n-3)/6], {n, 100}] (* _Wesley Ivan Hurt_, Sep 08 2015 *)
%t A047310 LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7}, 70] (* _Vincenzo Librandi_, Sep 10 2015 *)
%t A047310 Select[Range[0,100],MemberQ[{0,1,3,4,5,6},Mod[#,7]]&] (* _Harvey P. Dale_, Dec 02 2024 *)
%o A047310 (Magma) [n+Floor((n-3)/6): n in [1..100]]; // _Wesley Ivan Hurt_, Sep 08 2015
%o A047310 (Magma) [n: n in [0..100] | n mod 7 in [0,1,3,4,5,6]]; // _Vincenzo Librandi_, Sep 10 2015
%Y A047310 Cf. A017005 (7n+2).
%K A047310 nonn,easy
%O A047310 1,3
%A A047310 _N. J. A. Sloane_
%E A047310 More terms from _Vincenzo Librandi_, Sep 10 2015