%I #9 Sep 30 2016 13:23:13

%S 1,2,3,4,5,8,9,10,11,14,15,16,17,20,21,22,23,24,27,28,29,30,33,34,35,

%T 36,39,40,41,42,45,46,47,48,49,52,53,54,55,58,59,60,61,64,65,66,67,68,

%U 71,72,73,74,77,78,79,80,83,84,85,86,89,90,91,92,93,96

%N Sums-complement of the Beatty sequence for 2*Pi.

%C See A276871 for a definition of sums-complement and guide to related sequences.

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%e The Beatty sequence for 2*Pi is A038130 = (0,6,12,18,25,31,37,...), with difference sequence s = A276861 = (6,6,6,7,6,6,6,7,6,6,7,...). The sums s(j)+s(j+1)+...+s(k) include (6,7,12,13,...), with complement (1,2,3,4,5,8,9,10,...).

%t z = 500; r = 2*Pi; b = Table[Floor[k*r], {k, 0, z}]; (* A038130 *)

%t t = Differences[b]; (* A276861 *)

%t c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];

%t u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];

%t w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w] (* A276878 *)

%Y Cf. A038130, A276861, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 27 2016