A276880 Sums-complement of the Beatty sequence for 1 + sqrt(3).

1, 4, 7, 12, 15, 18, 23, 26, 29, 34, 37, 42, 45, 48, 53, 56, 59, 64, 67, 70, 75, 78, 83, 86, 89, 94, 97, 100, 105, 108, 111, 116, 119, 124, 127, 130, 135, 138, 141, 146, 149, 154, 157, 160, 165, 168, 171, 176, 179, 182, 187, 190, 195, 198, 201, 206, 209, 212

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 1 + sqrt(3) is A054088 = (0,2,5,8,19,13,16,...), with difference sequence s = A007538 = (2,3,3,2,3,3,3,2,3,3,3,2,3,3,2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,10,11,13,...), with complement (1,4,7,12,15,18,23,...).
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A054088, A007538, A276871.

Programs

Mathematica

z = 500; r = 1 + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A054088 *)
t = Differences[b]; (* A007538 *)
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]  (* A276880 *)