A276223 Position of n^Pi in the joint ranking of {h^e} and {k^Pi}, h > 1, k > 1.

2, 4, 6, 9, 11, 14, 17, 19, 22, 24, 27, 30, 33, 35, 38, 41, 44, 47, 49, 52, 55, 58, 61, 64, 67, 70, 73, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 143, 146, 149, 152, 155, 158, 161, 165, 168, 171, 174

Offset

1,1

Links

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

Formula

a(n) = n + floor(n^(Pi/e)); the complement is given by n + floor(n^(e/Pi)).

Example

The first numbers in the joint ranking are
2^e < 2^Pi < 3^e < 3^Pi < 4^e < 4^Pi , so that a(n) = (2,4,6,...).

Mathematica

z = 150; r = N[E, 100]; s = N[Pi, 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}]]  (* A276223 *)
Flatten[Table[Position[w, v[[n]]], {n, 1, z}]]  (* A276224 *)

Crossrefs

Cf. A276224 (complement).

Sequence in context: A242137 A138326 A274214 * A288468 A271906 A050502

Adjacent sequences: A276220 A276221 A276222 * A276224 A276225 A276226

Keyword

nonn,easy

Author

Clark Kimberling, Sep 06 2016

Status

approved