A276875 Sums-complement of the Beatty sequence for e.

1, 4, 7, 12, 15, 18, 23, 26, 31, 34, 37, 42, 45, 50, 53, 56, 61, 64, 69, 72, 75, 80, 83, 88, 91, 94, 99, 102, 105, 110, 113, 118, 121, 124, 129, 132, 137, 140, 143, 148, 151, 156, 159, 162, 167, 170, 175, 178, 181, 186, 189, 194, 197, 200, 205, 208, 211, 216

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 e is A022843 = (0,2,5,8,10,13,16,...), with difference sequence s = A267859 = (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 (2,3,5,6,8,9,10,12,13,...), with complement (1,4,7,12,15,...).

Mathematica

z = 500; r = E; b = Table[Floor[k*r], {k, 0, z}]; (* A022843 *)
t = Differences[b]; (* A267859 *)
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]  (* A276875 *)

Crossrefs

Cf. A022843, A276859, A276871.

Sequence in context: A085048 A024813 A276880 * A310771 A310772 A244741

Adjacent sequences: A276872 A276873 A276874 * A276876 A276877 A276878

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2016

Status

approved