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%I #4 Sep 12 2016 17:10:10
%S 4,7,12,17,23,29,35,42,50,58,66,75,84,93,103,113,124,135,146,157,169,
%T 181,194,206,219,233,246,260,274,288,303,318,333,349,364,380,396,413,
%U 430,446,464,481,499,517,535,553,572,590,610,629,648,668,688,708,728
%N Position of n^s in the joint ranking of {h} and {k^s}, h >= 1, k >= 2, s = golden ratio = (1+sqrt(5))/2.
%H Clark Kimberling, <a href="/A276222/b276222.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = n + floor(n^s), n >= 2; the complement is given by n + floor(n^(1/s)), n >= 1.
%e The first numbers in the joint ranking are
%e 1 < 2 < 3 < 2^s < 4 < 5 < 3^s < 6 < 7 < 8 < 9 < 4^s, so that a(n) = (4,7,12,...).
%t z = 150; s = N[GoldenRatio, 100];
%t u = Table[n + Floor[n^s], {n, 2, z}];
%t v = Table[n + Floor[n^(1/s)], {n, 1, z^s}];
%t w = Union[u, v]; Flatten[Table[Position[w, u[[n]]], {n, 1, z}]]
%Y Cf. A276219, A276220.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Sep 06 2016
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