A276214 Position of n^r in the joint ranking of {h^r} and {k^s}, where r = sqrt(3), s = sqrt(5), h > 1, k > 1.

1, 3, 4, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 90

Offset

1,2

Links

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

Formula

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

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) = (1,3,4,6,8,...).

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. A276213 (complement).

Sequence in context: A291322 A322741 A161579 * A285206 A047416 A064724

Adjacent sequences: A276211 A276212 A276213 * A276215 A276216 A276217

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2016

Status

approved