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

1,2

Comments

See A276871 for a definition of sums-complement and guide to related sequences.

Links

Table of n, a(n) for n=1..58.

Index entries for sequences related to Beatty sequences

Example

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,...)

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 *)

Crossrefs

Cf. A022842, A276858, A276871.

Sequence in context: A310684 A087065 A001197 * A310685 A310686 A339637

Adjacent sequences: A276871 A276872 A276873 * A276875 A276876 A276877

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2016

Status

approved