A276220 - OEIS

%I #4 Sep 12 2016 17:09:50

%S 1,2,4,5,7,8,9,11,12,14,15,16,18,19,20,22,23,24,26,27,28,29,31,32,33,

%T 35,36,37,38,40,41,42,43,45,46,47,48,50,51,52,53,55,56,57,58,59,61,62,

%U 63,64,66,67,68,69,71,72,73,74,75,77,78,79,80,81,83,84

%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="/A276220/b276220.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n + floor(n^s), n >= 1; the complement is given by n + floor(n^(1/s)), n >= 2.

%e The first numbers in the joint ranking are

%e 1^r < 2^r < 2^s < 3^r < 4^r < 3^s < 5^r < 6^r < 7^r < 4^s, so that a(n) = (1, 2, 4, 5, 7,...).

%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. A276219 (complement).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 06 2016