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%I #9 Sep 24 2016 10:35:01
%S 1,3,4,6,7,8,10,11,13,14,15,17,18,19,21,22,23,25,26,27,28,30,31,32,34,
%T 35,36,37,39,40,41,42,44,45,46,47,49,50,51,52,54,55,56,57,58,60,61,62,
%U 63,65,66,67,68,70,71,72,73,74,76,77,78,79,80,82,83,84
%N Position of n^r 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="/A276218/b276218.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n + floor(n^(r/s)); the complement is given by n + floor(n^(s/r)).
%e The first numbers in the joint ranking are
%e 2^r < 2^s < 3^r < 4^r < 3^s < 5^r < 6^r, so that a(n) = (1,3,4,6,...).
%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. A276217 (complement).
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 01 2016
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