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%I #4 Sep 03 2016 23:58:41
%S 2,5,9,12,16,20,24,29,33,38,43,48,53,59,64,69,75,81,87,93,99,105,111,
%T 117,124,130,137,143,150,157,164,171,178,185,192,200,207,214,222,229,
%U 237,245,252,260,268,276,284,292,300,308,317,325,333,342,350,359
%N Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(3), s = sqrt(6), h > 1, k > 1.
%H Clark Kimberling, <a href="/A276217/b276217.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n + floor(n^(s/r)); the complement is given by n + floor(n^(r/s)).
%e The first numbers in the joint ranking are
%e 2^r < 2^s < 3^r < 4^r < 3^s < 5^r < 6^r < 7^r < 4^s, so that a(n) = (2,5,9,...).
%t z = 150; r = N[Sqrt[3], 100]; s = N[Sqrt[6], 100];
%t u = Table[n + Floor[n^(s/r)], {n, 2, z}];
%t v = Table[n + Floor[n^(r/s)], {n, 2, z^(s/r)}];
%t w = Union[u, v];
%t Flatten[Table[Position[w, u[[n]]], {n, 1, z}]] (* A276217 *)
%t Flatten[Table[Position[w, v[[n]]], {n, 1, z}]] (* A276218 *)
%Y Cf. A276218 (complement).
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 01 2016
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