A276883 Sums-complement of the Beatty sequence for 2 + sqrt(3).

1, 2, 5, 6, 9, 10, 13, 16, 17, 20, 21, 24, 25, 28, 31, 32, 35, 36, 39, 40, 43, 46, 47, 50, 51, 54, 57, 58, 61, 62, 65, 66, 69, 72, 73, 76, 77, 80, 81, 84, 87, 88, 91, 92, 95, 96, 99, 102, 103, 106, 107, 110, 113, 114, 117, 118, 121, 122, 125, 128, 129, 132

Offset: 1

Author

Clark Kimberling, Sep 27 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(3) is A003512 = (0,3,7,11,14,18,22,26,...), with difference sequence s = A276865 = (3,4,4,3,4,4,4,3,4,4,4,3,4,4,3,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,7,8,11,12,14,15,18,...), with complement (1,2,5,6,9,10,13,...).
		

Links

• Index entries for sequences related to Beatty sequences.

Crossrefs

Cf. A003512, A276865, A276871.

Programs

Mathematica

z = 500; r = 2 + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A003512 *)
t = Differences[b]; (* A276865 *)
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]  (* A276883 *)