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A276889
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Sums-complement of the Beatty sequence for sqrt(2) + sqrt(3).
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3
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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
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1,2
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COMMENTS
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See A276871 for a definition of sums-complement and guide to related sequences.
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LINKS
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EXAMPLE
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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,...).
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MATHEMATICA
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z = 500; r = Sqrt[2] + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A110117 *)
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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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