A276884 Sums-complement of the Beatty sequence for 2 + sqrt(5).

1, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 20, 23, 24, 27, 28, 31, 32, 35, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 92, 95, 96, 99, 100, 103, 104, 107, 108, 109, 112, 113, 116, 117

Offset: 1

Author

Clark Kimberling, Oct 01 2016

Keywords

• nonn
• easy

Comments

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

Examples

			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
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A004976, A276866, A276871.

Programs

Mathematica

z = 500; r = 2 + Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A004076 *)
t = Differences[b]; (* A276866 *)
c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];
u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];
w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w];  (* A276884 *)