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A276888 Sums-complement of the Beatty sequence for 2 + sqrt(1/2). 4
1, 4, 7, 12, 15, 20, 23, 26, 31, 34, 39, 42, 45, 50, 53, 58, 61, 66, 69, 72, 77, 80, 85, 88, 91, 96, 99, 104, 107, 112, 115, 118, 123, 126, 131, 134, 137, 142, 145, 150, 153, 156, 161, 164, 169, 172, 177, 180, 183, 188, 191, 196, 199, 202, 207, 210, 215, 218 (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 2 + sqrt(1/2) is A182969 = (0,2,5,8,10,13,16,18,21,...), with difference sequence s = A276869 = (2,3,3,2,3,3,2,3,3,3,2,3,3,2,3,3,3,2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,10,11,13,14,16,...), with complement (1,4,7,12,15,20,23,...).

MATHEMATICA

z = 500; r = 2 + Sqrt[1/2]; b = Table[Floor[k*r], {k, 0, z}]; (* A182769 *)

t = Differences[b]; (* A276869 *)

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];  (* A276888 *)

CROSSREFS

Cf. A182769, A276869, A276871.

Sequence in context: A049509 A026360 A237514 * A047535 A310773 A310774

Adjacent sequences:  A276885 A276886 A276887 * A276889 A276890 A276891

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 01 2016

STATUS

approved

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)