A276876 Sums-complement of the Beatty sequence for 2e.

1, 2, 3, 4, 7, 8, 9, 12, 13, 14, 15, 18, 19, 20, 23, 24, 25, 26, 29, 30, 31, 34, 35, 36, 37, 40, 41, 42, 45, 46, 47, 50, 51, 52, 53, 56, 57, 58, 61, 62, 63, 64, 67, 68, 69, 72, 73, 74, 75, 78, 79, 80, 83, 84, 85, 88, 89, 90, 91, 94, 95, 96, 99, 100, 101, 102

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 2e is A276853 = (0,5,10,16,21,27,32,...), with difference sequence s = A276860 = (5,5,6,5,6,5,6,5,5,6,5,6,5,6,5,5,...).  The sums s(j)+s(j+1)+...+s(k) include (5,6,7,10,11,16,17,...), with complement (1,2,3,4,7,8,9,12,...).

Mathematica

z = 500; r = 2E; b = Table[Floor[k*r], {k, 0, z}]; (* A276853 *)
t = Differences[b]; (* A276860 *)
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]  (* A276876 *)

Crossrefs

Cf. A276853, A276860, A276871.

Sequence in context: A145487 A061856 A105941 * A047202 A064953 A097503

Adjacent sequences: A276873 A276874 A276875 * A276877 A276878 A276879

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2016

Status

approved