A276220 Position of n^s in the joint ranking of {h} and {k^s}, where s = sqrt(2), h >= 1, k >= 2.

1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

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. A276219 (complement).

Sequence in context: A183862 A254058 A346128 * A288204 A047381 A286428

Adjacent sequences: A276217 A276218 A276219 * A276221 A276222 A276223

Keyword

nonn,easy

Author

Clark Kimberling, Sep 06 2016

Status

approved