%I
%S 1,2,3,6,7,10,11,14,15,18,19,20,23,24,27,28,31,32,35,36,37,40,41,44,
%T 45,48,49,52,53,54,57,58,61,62,65,66,69,70,71,74,75,78,79,82,83,86,87,
%U 90,91,92,95,96,99,100,103,104,107,108,109,112,113,116,117
%N Sumscomplement of the Beatty sequence for 2 + 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 2 + sqrt(5) is A004976 = (0,4,8,12,16,21,25,29, 33,38,42,46,50,55,59,63,...) with difference sequence s = A276866 = (4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,...). The sums s(j)+s(j+1)+...+s(k) include (4,5,8,9,12,13,16,...), with complement (1,2,3,6,7,10,11,14,...).  corrected by _Michel Dekking_, Jan 30 2017
%t z = 500; r = 2 + Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A004076 *)
%t t = Differences[b]; (* A276866 *)
%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]; (* A276884 *)
%Y Cf. A004976, A276866, A276871.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Oct 01 2016
