A276221 Position of n^s in the joint ranking of {h} and {k^s}, s = sqrt(3), h >= 1, k >= 2.

4, 8, 14, 20, 27, 35, 43, 52, 62, 73, 84, 96, 109, 122, 136, 151, 166, 182, 198, 215, 232, 250, 268, 287, 307, 327, 348, 369, 390, 412, 435, 458, 482, 506, 531, 556, 581, 607, 634, 661, 688, 716, 745, 774, 803, 833, 863, 894, 925, 956, 989, 1021, 1054, 1087

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Formula

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

Mathematica

z = 150; s = N[Sqrt[3], 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}]]

Crossrefs

Cf. A276219.

Sequence in context: A049420 A232996 A317292 * A265284 A055507 A343880

Adjacent sequences: A276218 A276219 A276220 * A276222 A276223 A276224

Keyword

nonn,easy

Author

Clark Kimberling, Sep 06 2016

Status

approved