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A276883 Sums-complement of the Beatty sequence for 2 + sqrt(3). 3
1, 2, 5, 6, 9, 10, 13, 16, 17, 20, 21, 24, 25, 28, 31, 32, 35, 36, 39, 40, 43, 46, 47, 50, 51, 54, 57, 58, 61, 62, 65, 66, 69, 72, 73, 76, 77, 80, 81, 84, 87, 88, 91, 92, 95, 96, 99, 102, 103, 106, 107, 110, 113, 114, 117, 118, 121, 122, 125, 128, 129, 132 (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..62.

Index entries for sequences related to Beatty sequences)

EXAMPLE

The Beatty sequence for 2 + sqrt(3) is A003512 = (0,3,7,11,14,18,22,26,...), with difference sequence s = A276865 = (3,4,4,3,4,4,4,3,4,4,4,3,4,4,3,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,7,8,11,12,14,15,18,...), with complement (1,2,5,6,9,10,13,...).

MATHEMATICA

z = 500; r = 2 + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A003512 *)

t = Differences[b]; (* A276865 *)

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]  (* A276883 *)

CROSSREFS

Cf. A003512, A276865, A276871.

Sequence in context: A327220 A166097 A285502 * A288552 A187583 A000277

Adjacent sequences:  A276880 A276881 A276882 * A276884 A276885 A276886

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 27 2016

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)