A276211 - OEIS

A276211

Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(2), s = sqrt(5), h > 1, k > 1.

2, 6, 10, 15, 20, 26, 32, 39, 46, 53, 60, 68, 76, 85, 94, 103, 112, 122, 132, 142, 152, 163, 174, 185, 196, 208, 220, 232, 244, 257, 269, 282, 295, 309, 322, 336, 350, 364, 379, 393, 408, 423, 438, 454, 469, 485, 501, 517, 533, 550, 566, 583, 600, 617, 634

(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 < 5^r < 3^s < 6^r < 7^r < 8^r < 4^s < 9^r, so that a(n) = (2,6,10,...).

MATHEMATICA

z = 150; r = N[Sqrt[2], 100]; s = N[Sqrt[5], 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}]] (* A276211 *)

Flatten[Table[Position[w, v[[n]]], {n, 1, z}]] (* A276212 *)

CROSSREFS

Cf. A276212 (complement).

Sequence in context: A179777 A285959 A288631 * A190091 A343148 A331250

Adjacent sequences: A276208 A276209 A276210 * A276212 A276213 A276214

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 01 2016

STATUS

approved

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