A276217 Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(3), s = sqrt(6), h > 1, k > 1.

2, 5, 9, 12, 16, 20, 24, 29, 33, 38, 43, 48, 53, 59, 64, 69, 75, 81, 87, 93, 99, 105, 111, 117, 124, 130, 137, 143, 150, 157, 164, 171, 178, 185, 192, 200, 207, 214, 222, 229, 237, 245, 252, 260, 268, 276, 284, 292, 300, 308, 317, 325, 333, 342, 350, 359

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Formula

a(n) = n + floor(n^(s/r)); the complement is given by n + floor(n^(r/s)).

Example

The first numbers in the joint ranking are
2^r < 2^s < 3^r < 4^r < 3^s < 5^r < 6^r < 7^r < 4^s, so that a(n) = (2,5,9,...).

Mathematica

z = 150; r = N[Sqrt[3], 100]; s = N[Sqrt[6], 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}]]  (* A276217 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276218 *)

Crossrefs

Cf. A276218 (complement).

Sequence in context: A284624 A086814 A211274 * A354835 A086343 A056549

Adjacent sequences: A276214 A276215 A276216 * A276218 A276219 A276220

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2016

Status

approved