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%I #4 Sep 03 2016 23:58:28
%S 3,7,13,19,26,34,42,51,61,72,83,95,108,121,135,150,165,181,197,214,
%T 231,249,267,286,306,326,347,368,389,411,434,457,481,505,530,555,580,
%U 606,633,660,687,715,744,773,802,832,862,893,924,955,988,1020,1053,1086
%N Position of n^s 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="/A276215/b276215.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 < 3^r < 2^s < 4^r < 5^r < 6^r < 3^s, so that a(n) = (3,7,...).
%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. A276216 (complement).
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 01 2016
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