A276224 Position of n^e in the joint ranking of {h^e} and {k^Pi}, h > 1, k > 1.

1, 3, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101

Offset

1,2

Links

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

Formula

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

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) = (1,3,5,...).

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. A276223 (complement).

Sequence in context: A109404 A221056 A288467 * A186342 A186315 A285074

Adjacent sequences: A276221 A276222 A276223 * A276225 A276226 A276227

Keyword

nonn,easy

Author

Clark Kimberling, Sep 06 2016

Status

approved