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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. 2
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 (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 < 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: A039185 A080240 A135668 * A226946 A288708 A039138

Adjacent sequences:  A276213 A276214 A276215 * A276217 A276218 A276219

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 01 2016

STATUS

approved

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Last modified December 10 23:29 EST 2019. Contains 329910 sequences. (Running on oeis4.)