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A276882 Sums-complement of the Beatty sequence for 2 + sqrt(2). 3
1, 2, 5, 8, 9, 12, 15, 16, 19, 22, 25, 26, 29, 32, 33, 36, 39, 42, 43, 46, 49, 50, 53, 56, 57, 60, 63, 66, 67, 70, 73, 74, 77, 80, 83, 84, 87, 90, 91, 94, 97, 98, 101, 104, 107, 108, 111, 114, 115, 118, 121, 124, 125, 128, 131, 132, 135, 138, 141, 142, 145 (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..61.

Index entries for sequences related to Beatty sequences

EXAMPLE

The Beatty sequence for 2 + sqrt(2) is A001952 = (0,3,6,10,13,17,20, 23,27,...), with difference sequence s = A276864 = (3,3,4,3,4,3,3,4,3,4,3,3,4,3,4,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,10,11,13,14,17,...), with complement (1,2,5,8,9,12,15,...).

MATHEMATICA

z = 500; r = 2+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A001952 *)

t = Differences[b]; (* A276864 *)

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]  (* A276882 *)

CROSSREFS

Cf. A001952, A276864, A276871.

Sequence in context: A289628 A047387 A063282 * A045928 A190768 A184866

Adjacent sequences:  A276879 A276880 A276881 * A276883 A276884 A276885

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 27 2016

STATUS

approved

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Last modified December 10 12:30 EST 2019. Contains 329895 sequences. (Running on oeis4.)