A276218 Position of n^r in the joint ranking of {h^r} and {k^s}, where r = sqrt(3), s = sqrt(6), h > 1, k > 1.

1, 3, 4, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84

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 < 6^r, so that a(n) = (1,3,4,6,...).

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. A276217 (complement).

Sequence in context: A361457 A247987 A062975 * A047299 A186159 A184578

Adjacent sequences: A276215 A276216 A276217 * A276219 A276220 A276221

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2016

Status

approved