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A276880 Sums-complement of the Beatty sequence for 1 + sqrt(3). 2
1, 4, 7, 12, 15, 18, 23, 26, 29, 34, 37, 42, 45, 48, 53, 56, 59, 64, 67, 70, 75, 78, 83, 86, 89, 94, 97, 100, 105, 108, 111, 116, 119, 124, 127, 130, 135, 138, 141, 146, 149, 154, 157, 160, 165, 168, 171, 176, 179, 182, 187, 190, 195, 198, 201, 206, 209, 212 (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..58.

Index entries for sequences related to Beatty sequences

EXAMPLE

The Beatty sequence for 1 + sqrt(3) is A054088 = (0,2,5,8,19,13,16,...), with difference sequence s = A007538 = (2,3,3,2,3,3,3,2,3,3,3,2,3,3,2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,10,11,13,...), with complement (1,4,7,12,15,18,23,...).

MATHEMATICA

z = 500; r = 1 + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A054088 *)

t = Differences[b]; (* A007538 *)

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]  (* A276880 *)

CROSSREFS

Cf. A054088, A007538, A276871.

Sequence in context: A161843 A085048 A024813 * A276875 A310771 A310772

Adjacent sequences:  A276877 A276878 A276879 * A276881 A276882 A276883

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 27 2016

STATUS

approved

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)