A276212 - OEIS

%I #4 Sep 03 2016 23:58:06

%S 1,3,4,5,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,25,27,28,29,30,31,

%T 33,34,35,36,37,38,40,41,42,43,44,45,47,48,49,50,51,52,54,55,56,57,58,

%U 59,61,62,63,64,65,66,67,69,70,71,72,73,74,75,77,78,79

%N Position of n^r in the joint ranking of {h^r} and {k^s}, where r = sqrt(2), s = sqrt(5), h > 1, k > 1.

%H Clark Kimberling, <a href="/A276212/b276212.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 < 2^s < 3^r < 4^r < 5^r < 3^s < 6^r < 7^r < 8^r < 4^s < 9^r, so that a(n) = (1,3,4,5,7,...).

%t z = 150; r = N[Sqrt[2], 100]; s = N[Sqrt[5], 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}]]  (* A276211 *)

%t Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276212 *)

%Y Cf. A276211 (complement).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 01 2016