A276888 Sums-complement of the Beatty sequence for 2 + sqrt(1/2).

1, 4, 7, 12, 15, 20, 23, 26, 31, 34, 39, 42, 45, 50, 53, 58, 61, 66, 69, 72, 77, 80, 85, 88, 91, 96, 99, 104, 107, 112, 115, 118, 123, 126, 131, 134, 137, 142, 145, 150, 153, 156, 161, 164, 169, 172, 177, 180, 183, 188, 191, 196, 199, 202, 207, 210, 215, 218

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 2 + sqrt(1/2) is A182969 = (0,2,5,8,10,13,16,18,21,...), with difference sequence s = A276869 = (2,3,3,2,3,3,2,3,3,3,2,3,3,2,3,3,3,2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,10,11,13,14,16,...), with complement (1,4,7,12,15,20,23,...).
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A182769, A276869, A276871.

Programs

Mathematica

z = 500; r = 2 + Sqrt[1/2]; b = Table[Floor[k*r], {k, 0, z}]; (* A182769 *)
t = Differences[b]; (* A276869 *)
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];  (* A276888 *)