A276872 Sums-complement of the Beatty sequence for sqrt(6).

1, 6, 11, 16, 21, 28, 33, 38, 43, 50, 55, 60, 65, 70, 77, 82, 87, 92, 99, 104, 109, 114, 119, 126, 131, 136, 141, 148, 153, 158, 163, 168, 175, 180, 185, 190, 197, 202, 207, 212, 217, 224, 229, 234, 239, 246, 251, 256, 261, 268, 273, 278, 283, 288, 295, 300

Offset: 1

Author

Clark Kimberling, Sep 26 2016

Keywords

• nonn
• easy

Comments

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

Examples

			The Beatty sequence for sqrt(6) is A022840 = (0, 2, 4, 7, 9, 12, 14, 17,...), with difference sequence s = A276856 = (2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,4,5,7,8,9,10,12,...), with complement (1,6,11,16,21,...).
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A022840, A276856, A276871.

Programs

Mathematica

z = 500; r = Sqrt[6]; b = Table[Floor[k*r], {k, 0, z}]; (* A022840 *)
t = Differences[b]; (* A276856 *)
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];  (* A276872 *)