A276209 Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(2), s = sqrt(3), h > 1, k > 1.

2, 4, 7, 10, 12, 15, 18, 21, 24, 27, 30, 34, 37, 40, 43, 47, 50, 53, 57, 60, 64, 67, 71, 74, 78, 81, 85, 88, 92, 96, 99, 103, 107, 110, 114, 118, 122, 125, 129, 133, 137, 141, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + floor(n^(s/r)), with complement given by n + floor(n^(r/s)).

Example

The first numbers in the joint ranking are
2^r < 2^s < 3^r < 3^s < 4^r < 5^r < 4^s, so that a(n) = (2,4,7,...).

Mathematica

z = 150; r = N[Sqrt[2], 100]; s = N[Sqrt[3], 100];
u = Table[n + Floor[n^(s/r)], {n, 2, z}];
v = Table[n + Floor[n^(r/s)], {n, 2, z^(s/r)}];
w = Union[u, v];
Flatten[Table[Position[w, u[[n]]], {n, 1, z}]]  (* A276209 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276210 *)

Crossrefs

Cf. A276210 (complement).

Sequence in context: A186224 A008062 A089972 * A062429 A007087 A101359

Adjacent sequences: A276206 A276207 A276208 * A276210 A276211 A276212

Keyword

nonn,easy

Author

Clark Kimberling, Aug 31 2016

Status

approved