A276215 Position of n^s in the joint ranking of {h^r} and {k^s}, where r = sqrt(2), s = sqrt(6), h > 1, k > 1.

3, 7, 13, 19, 26, 34, 42, 51, 61, 72, 83, 95, 108, 121, 135, 150, 165, 181, 197, 214, 231, 249, 267, 286, 306, 326, 347, 368, 389, 411, 434, 457, 481, 505, 530, 555, 580, 606, 633, 660, 687, 715, 744, 773, 802, 832, 862, 893, 924, 955, 988, 1020, 1053, 1086

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

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. A276216 (complement).

Sequence in context: A278448 A117679 A310265 * A202117 A100458 A193765

Adjacent sequences: A276212 A276213 A276214 * A276216 A276217 A276218

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2016

Status

approved