A276881 Sums-complement of the Beatty sequence for 1 + sqrt(5).

1, 2, 5, 8, 11, 14, 15, 18, 21, 24, 27, 28, 31, 34, 37, 40, 41, 44, 47, 50, 53, 54, 57, 60, 63, 66, 69, 70, 73, 76, 79, 82, 83, 86, 89, 92, 95, 96, 99, 102, 105, 108, 109, 112, 115, 118, 121, 124, 125, 128, 131, 134, 137, 138, 141, 144, 147, 150, 151, 154

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(5) is A276854 = (0,3,6,9,12,16,19,...), with difference sequence s = A276863 = (3,3,3,3,4,3,3,3,4,3,3,3,4,3,3,3,4,...).  The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,9,10,12,13,...), with complement (1,2,5,8,11,14,15,,...).
		

Links

• Index entries for sequences related to Beatty sequences

Crossrefs

Cf. A276854, A276863, A276871.

Programs

Mathematica

z = 500; r = 1+ Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A276854 *)
t = Differences[b]; (* A276863 *)
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]  (* A276881 *)