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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
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 (list; graph; refs; listen; history; text; internal format)
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 * A086343 A056549 A034806

Adjacent sequences:  A276214 A276215 A276216 * A276218 A276219 A276220

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 01 2016

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)