%I
%S 1,2,5,8,11,14,15,18,21,24,27,28,31,34,37,40,41,44,47,50,53,54,57,60,
%T 63,66,69,70,73,76,79,82,83,86,89,92,95,96,99,102,105,108,109,112,115,
%U 118,121,124,125,128,131,134,137,138,141,144,147,150,151,154
%N Sumscomplement of the Beatty sequence for 1 + sqrt(5).
%C See A276871 for a definition of sumscomplement 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 1 + sqrt(5) is A276854 = (0,3,6,9,12,16,19,...), with difference sequence s = A276863 = (3,3,3,3,4,3,3,3,4,3,3,3,4,3,3,3,4,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,9,10,12,13,...), with complement (1,2,5,8,11,14,15,,...).
%t z = 500; r = 1+ Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A276854 *)
%t t = Differences[b]; (* A276863 *)
%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] (* A276881 *)
%Y Cf. A276854, A276863, A276871.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 27 2016
