A276219 Position of n^s in the joint ranking of {h} and {k^s}, where s = sqrt(2), h >= 1, k >= 2.

3, 6, 10, 13, 17, 21, 25, 30, 34, 39, 44, 49, 54, 60, 65, 70, 76, 82, 88, 94, 100, 106, 112, 118, 125, 131, 138, 144, 151, 158, 165, 172, 179, 186, 193, 201, 208, 215, 223, 230, 238, 246, 253, 261, 269, 277, 285, 293, 301, 309, 318, 326, 334, 343, 351, 360

Offset

2,1

Links

Clark Kimberling, Table of n, a(n) for n = 2..10001 (offset adapted by Georg Fischer, Jan 24 2019)

Formula

a(n) = n - 1 + floor(n^s), n >= 2; the complement is given by n + floor(n^(1/s)), n >= 1.

Example

The first numbers in the joint ranking are
1 < 2 < 2^s < 3 < 4 < 3^s < 5 < 6 < 7 < 4^s, so that a(n) = (3,6,10,...).

Mathematica

z = 150; s = N[Sqrt[2], 100];
u = Table[n + Floor[n^(s)], {n, 2, z}];
v = Table[n + Floor[n^(1/s)], {n, 1, z^s}];
w = Union[u, v];
Flatten[Table[Position[w, u[[n]]], {n, 1, z}]]  (* A276219 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276220 *)

Crossrefs

Cf. A276220 (complement).

Sequence in context: A189524 A288205 A049880 * A267593 A248221 A189368

Adjacent sequences: A276216 A276217 A276218 * A276220 A276221 A276222

Keyword

nonn,easy

Author

Clark Kimberling, Sep 06 2016

Extensions

Edited by Clark Kimberling, Nov 06 2018

Status

approved