A276889 - OEIS

A276889

Sums-complement of the Beatty sequence for sqrt(2) + sqrt(3).

1, 2, 5, 8, 11, 14, 17, 20, 21, 24, 27, 30, 33, 36, 39, 42, 43, 46, 49, 52, 55, 58, 61, 64, 65, 68, 71, 74, 77, 80, 83, 86, 87, 90, 93, 96, 99, 102, 105, 108, 109, 112, 115, 118, 121, 124, 127, 130, 131, 134, 137, 140, 143, 146, 149, 150, 153, 156, 159, 162

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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..60.

Index entries for sequences related to Beatty sequences

EXAMPLE

The Beatty sequence for sqrt(2) + sqrt(3) is A110117 = (0,3,6,9,12,15,18,22,...), with difference sequence s = A276870 = (3,3,3,3,3,3,4,3,3,3,3,3,3,4,3,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,9,10,...), with complement (1,2,5,8,11,14,17,20,21,...).

MATHEMATICA

z = 500; r = Sqrt[2] + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A110117 *)

t = Differences[b]; (* A276870 *)

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]; (* A276889 *)

CROSSREFS

Cf. A110117, A276870, A276871.

Sequence in context: A109232 A064718 A190336 * A276877 A329961 A078608

Adjacent sequences: A276886 A276887 A276888 * A276890 A276891 A276892

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 01 2016

STATUS

approved