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A276873 Sums-complement of the Beatty sequence for sqrt(7). 3
1, 4, 9, 12, 17, 20, 25, 28, 33, 36, 41, 46, 49, 54, 57, 62, 65, 70, 73, 78, 81, 86, 91, 94, 99, 102, 107, 110, 115, 118, 123, 128, 131, 136, 139, 144, 147, 152, 155, 160, 163, 168, 173, 176, 181, 184, 189, 192, 197, 200, 205, 208, 213, 218, 221, 226, 229 (list; graph; refs; listen; history; text; internal format)
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..57.

Index entries for sequences related to Beatty sequences

EXAMPLE

The Beatty sequence for sqrt(7) is A022841 = (0,2,5,7,10,13,...), with difference sequence s = A276857 = (2,3,2,3,3,2,3,3,2,3,3,2,3,3,2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,6,7,8,10,11,13,...), with complement (1,4,9,12,17,...).

MATHEMATICA

z = 500; r = Sqrt[7]; b = Table[Floor[k*r], {k, 0, z}]; (* A022841 *)

t = Differences[b]; (* A276857 *)

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]  (* A276873 *)

CROSSREFS

Cf. A022841, A276857, A276871.

Sequence in context: A330879 A285419 A047461 * A190448 A312860 A312861

Adjacent sequences:  A276870 A276871 A276872 * A276874 A276875 A276876

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 27 2016

STATUS

approved

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Last modified September 27 00:14 EDT 2020. Contains 337378 sequences. (Running on oeis4.)