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%I #4 Sep 03 2016 23:58:35
%S 1,2,4,5,6,8,9,10,11,12,14,15,16,17,18,20,21,22,23,24,25,27,28,29,30,
%T 31,32,33,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,52,53,54,55,56,
%U 57,58,59,60,62,63,64,65,66,67,68,69,70,71,73,74,75,76
%N Position of n^r in the joint ranking of {h^r} and {k^s}, where r = sqrt(2), s = sqrt(6), h > 1, k > 1.
%H Clark Kimberling, <a href="/A276216/b276216.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 < 3^r < 2^s < 4^r < 5^r < 6^r < 3^s, so that a(n) = (1,2,4,5,6,...).
%t z = 150; r = N[Sqrt[2], 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}]] (* A276215 *)
%t Flatten[Table[Position[w, v[[n]]], {n, 1, z}]] (* A276216 *)
%Y Cf. A276215 (complement).
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 01 2016
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