A276874 Sums-complement of the Beatty sequence for sqrt(8).

1, 4, 7, 10, 13, 18, 21, 24, 27, 30, 35, 38, 41, 44, 47, 52, 55, 58, 61, 64, 69, 72, 75, 78, 81, 86, 89, 92, 95, 100, 103, 106, 109, 112, 117, 120, 123, 126, 129, 134, 137, 140, 143, 146, 151, 154, 157, 160, 163, 168, 171, 174, 177, 180, 185, 188, 191, 194

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 sqrt(8) is A022842 = (0,2,5,8,11,14,16,...), with difference sequence s = A276858 = (2,3,3,3,3,2,3,3,3,3,3,2,3,3,3,3,3,2,3,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,11,12, 14,...), with complement (1,4,7,10,13,18,...)
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A022842, A276858, A276871.

Programs

Mathematica

z = 500; r = Sqrt[8]; b = Table[Floor[k*r], {k, 0, z}]; (* A022842 *)
t = Differences[b]; (* A276858 *)
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]  (* A276874 *)