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A276874 Sums-complement of the Beatty sequence for sqrt(8). 3
1, 4, 7, 10, 13, 18, 21, 24, 27, 30, 35, 38, 41, 44, 47, 52, 55, 58, 61, 64, 69, 72, 75, 78, 81, 86, 89, 92, 95, 100, 103, 106, 109, 112, 117, 120, 123, 126, 129, 134, 137, 140, 143, 146, 151, 154, 157, 160, 163, 168, 171, 174, 177, 180, 185, 188, 191, 194 (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 sqrt(8) is A022842 = (0,2,5,8,11,14,16,...), with difference sequence s = A276858 = (2,3,3,3,3,2,3,3,3,3,3,2,3,3,3,3,3,2,3,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,11,12, 14,...), with complement (1,4,7,10,13,18,...)

MATHEMATICA

z = 500; r = Sqrt[8]; b = Table[Floor[k*r], {k, 0, z}]; (* A022842 *)

t = Differences[b]; (* A276858 *)

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]  (* A276874 *)

CROSSREFS

Cf. A022842, A276858, A276871.

Sequence in context: A310684 A087065 A001197 * A310685 A310686 A173178

Adjacent sequences:  A276871 A276872 A276873 * A276875 A276876 A276877

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 27 2016

STATUS

approved

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Last modified February 21 19:40 EST 2019. Contains 320376 sequences. (Running on oeis4.)