A276216 Position of n^r in the joint ranking of {h^r} and {k^s}, where r = sqrt(2), s = sqrt(6), h > 1, k > 1.

1, 2, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76

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 < 3^r < 2^s < 4^r < 5^r < 6^r < 3^s, so that a(n) = (1,2,4,5,6,...).

Mathematica

z = 150; r = N[Sqrt[2], 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}]]  (* A276215 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276216 *)

Crossrefs

Cf. A276215 (complement).

Sequence in context: A080240 A345443 A135668 * A226946 A288708 A039138

Adjacent sequences: A276213 A276214 A276215 * A276217 A276218 A276219

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2016

Status

approved