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A276213
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Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(3), s = sqrt(5), h > 1, k > 1.
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2
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2, 5, 7, 10, 14, 17, 20, 24, 27, 31, 34, 38, 42, 45, 49, 53, 57, 61, 65, 69, 74, 78, 82, 86, 91, 95, 99, 104, 108, 113, 117, 122, 126, 131, 136, 140, 145, 150, 155, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 245, 250
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = n + floor(n^(s/r)); the complement is given by n + floor(n^(r/s)).
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EXAMPLE
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The first numbers in the joint ranking are
2^r < 2^s < 3^r < 4^r < 3^s < 5^r < 4^s < 6^r, so that a(n) = (2,5,7,...).
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MATHEMATICA
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z = 150; r = N[Sqrt[3], 100]; s = N[Sqrt[5], 100];
u = Table[n + Floor[n^(s/r)], {n, 2, z}];
v = Table[n + Floor[n^(r/s)], {n, 2, z^(s/r)}];
w = Union[u, v];
Flatten[Table[Position[w, u[[n]]], {n, 1, z}]] (* A276213 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]] (* A276214 *)
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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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