A276882 Sums-complement of the Beatty sequence for 2 + sqrt(2).

1, 2, 5, 8, 9, 12, 15, 16, 19, 22, 25, 26, 29, 32, 33, 36, 39, 42, 43, 46, 49, 50, 53, 56, 57, 60, 63, 66, 67, 70, 73, 74, 77, 80, 83, 84, 87, 90, 91, 94, 97, 98, 101, 104, 107, 108, 111, 114, 115, 118, 121, 124, 125, 128, 131, 132, 135, 138, 141, 142, 145

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(2) is A001952 = (0,3,6,10,13,17,20, 23,27,...), with difference sequence s = A276864 = (3,3,4,3,4,3,3,4,3,4,3,3,4,3,4,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,10,11,13,14,17,...), with complement (1,2,5,8,9,12,15,...).
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A001952, A276864, A276871.

Programs

Mathematica

z = 500; r = 2+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A001952 *)
t = Differences[b]; (* A276864 *)
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]  (* A276882 *)