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Position of n^s in the joint ranking of {h} and {k^s}, where s = sqrt(2), h >= 1, k >= 2.
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%I #13 Jan 25 2019 03:26:55

%S 3,6,10,13,17,21,25,30,34,39,44,49,54,60,65,70,76,82,88,94,100,106,

%T 112,118,125,131,138,144,151,158,165,172,179,186,193,201,208,215,223,

%U 230,238,246,253,261,269,277,285,293,301,309,318,326,334,343,351,360

%N Position of n^s in the joint ranking of {h} and {k^s}, where s = sqrt(2), h >= 1, k >= 2.

%H Clark Kimberling, <a href="/A276219/b276219.txt">Table of n, a(n) for n = 2..10001</a> (offset adapted by _Georg Fischer_, Jan 24 2019)

%F a(n) = n - 1 + 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 < 2^s < 3 < 4 < 3^s < 5 < 6 < 7 < 4^s, so that a(n) = (3,6,10,...).

%t z = 150; s = N[Sqrt[2], 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];

%t Flatten[Table[Position[w, u[[n]]], {n, 1, z}]] (* A276219 *)

%t Flatten[Table[Position[w, v[[n]]], {n, 1, z}]] (* A276220 *)

%Y Cf. A276220 (complement).

%K nonn,easy

%O 2,1

%A _Clark Kimberling_, Sep 06 2016

%E Edited by _Clark Kimberling_, Nov 06 2018