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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A042954 A247987 A062975 * A047299 A186159 A184578

Adjacent sequences:  A276215 A276216 A276217 * A276219 A276220 A276221

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 01 2016

STATUS

approved

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Last modified April 12 21:13 EDT 2021. Contains 342932 sequences. (Running on oeis4.)