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A276872
Sums-complement of the Beatty sequence for sqrt(6).
3
1, 6, 11, 16, 21, 28, 33, 38, 43, 50, 55, 60, 65, 70, 77, 82, 87, 92, 99, 104, 109, 114, 119, 126, 131, 136, 141, 148, 153, 158, 163, 168, 175, 180, 185, 190, 197, 202, 207, 212, 217, 224, 229, 234, 239, 246, 251, 256, 261, 268, 273, 278, 283, 288, 295, 300
OFFSET
1,2
COMMENTS
See A276871 for a definition of sums-complement and guide to related sequences.
EXAMPLE
The Beatty sequence for sqrt(6) is A022840 = (0, 2, 4, 7, 9, 12, 14, 17,...), with difference sequence s = A276856 = (2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2,...). The sums s(j)+s(j+1)+...+s(k) include (2,3,4,5,7,8,9,10,12,...), with complement (1,6,11,16,21,...).
MATHEMATICA
z = 500; r = Sqrt[6]; b = Table[Floor[k*r], {k, 0, z}]; (* A022840 *)
t = Differences[b]; (* A276856 *)
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]; (* A276872 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 26 2016
STATUS
approved