A276887 Sums-complement of the Beatty sequence for 3 + tau.

1, 2, 3, 6, 7, 8, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 29, 30, 31, 34, 35, 38, 39, 40, 43, 44, 45, 48, 49, 52, 53, 54, 57, 58, 59, 62, 63, 66, 67, 68, 71, 72, 75, 76, 77, 80, 81, 82, 85, 86, 89, 90, 91, 94, 95, 98, 99, 100, 103, 104, 105, 108, 109, 112

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 3 + tau is A276855 = (-,4,9,13,18,23,27,...), with difference sequence s = A276868 = (4,5,4,5,5,4,5,4,5,5,4,5,5,4,5,4,...).  The sums s(j)+s(j+1)+...+s(k) include (4,5,9,10,13,14,18,...), with complement (1,2,3,6,7,8,11,12,15,...).
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A276855, A276868, A276871.

Programs

Mathematica

z = 500; r = 3 + GoldenRatio; b = Table[Floor[k*r], {k, 0, z}]; (* A276855 *)
t = Differences[b]; (* A276868 *)
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];  (* A276887 *)