A276878 Sums-complement of the Beatty sequence for 2*Pi.

1, 2, 3, 4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, 33, 34, 35, 36, 39, 40, 41, 42, 45, 46, 47, 48, 49, 52, 53, 54, 55, 58, 59, 60, 61, 64, 65, 66, 67, 68, 71, 72, 73, 74, 77, 78, 79, 80, 83, 84, 85, 86, 89, 90, 91, 92, 93, 96

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..66.

Index entries for sequences related to Beatty sequences

Example

The Beatty sequence for 2*Pi is A038130 = (0,6,12,18,25,31,37,...), with difference sequence s = A276861 = (6,6,6,7,6,6,6,7,6,6,7,...).  The sums s(j)+s(j+1)+...+s(k) include (6,7,12,13,...), with complement (1,2,3,4,5,8,9,10,...).

Mathematica

z = 500; r = 2*Pi; b = Table[Floor[k*r], {k, 0, z}]; (* A038130 *)
t = Differences[b]; (* A276861 *)
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]  (* A276878 *)

Crossrefs

Cf. A038130, A276861, A276871.

Sequence in context: A155941 A046892 A068406 * A047247 A169606 A140769

Adjacent sequences: A276875 A276876 A276877 * A276879 A276880 A276881

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2016

Status

approved