A276213 Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(3), s = sqrt(5), h > 1, k > 1.

2, 5, 7, 10, 14, 17, 20, 24, 27, 31, 34, 38, 42, 45, 49, 53, 57, 61, 65, 69, 74, 78, 82, 86, 91, 95, 99, 104, 108, 113, 117, 122, 126, 131, 136, 140, 145, 150, 155, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 245, 250

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

Mathematica

z = 150; r = N[Sqrt[3], 100]; s = N[Sqrt[5], 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}]]  (* A276213 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276214 *)

Crossrefs

Cf. A276214 (complement).

Sequence in context: A267379 A287403 A287399 * A094019 A161580 A024177

Adjacent sequences: A276210 A276211 A276212 * A276214 A276215 A276216

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2016

Status

approved