|
%I #27 Sep 08 2022 08:44:56
%S 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 29,31,32,33,34,35,36,38,39,40,41,42,43,45,46,47,48,49,50,52,53,54,55,
%U 56,57,59,60,61,62,63,64,66,67,68,69,70,71,73,74,75,76,77,78
%N Numbers that are congruent to {0, 1, 3, 4, 5, 6} mod 7.
%C Complement of A017005. - _Michel Marcus_, Sep 08 2015
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1)
%F 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 From _Wesley Ivan Hurt_, Sep 08 2015: (Start)
%F a(n) = a(n-1)+a(n-6)-a(n-7) for n>7.
%F a(n) = n + floor((n-3)/6). (End)
%F From _Wesley Ivan Hurt_, Jun 15 2016: (Start)
%F 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 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:=n->n+floor((n-3)/6): seq(A047310(n), n=1..100); # _Wesley Ivan Hurt_, Sep 08 2015
%t Table[n+Floor[(n-3)/6], {n, 100}] (* _Wesley Ivan Hurt_, Sep 08 2015 *)
%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7}, 70] (* _Vincenzo Librandi_, Sep 10 2015 *)
%o (Magma) [n+Floor((n-3)/6): n in [1..100]]; // _Wesley Ivan Hurt_, Sep 08 2015
%o (Magma) [n: n in [0..100] | n mod 7 in [0,1,3,4,5,6]]; // _Vincenzo Librandi_, Sep 10 2015
%Y Cf. A017005 (7n+2).
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Sep 10 2015
|
