A182778 Beatty sequence for 3 + sqrt(3).

4, 9, 14, 18, 23, 28, 33, 37, 42, 47, 52, 56, 61, 66, 70, 75, 80, 85, 89, 94, 99, 104, 108, 113, 118, 123, 127, 132, 137, 141, 146, 151, 156, 160, 165, 170, 175, 179, 184, 189, 194, 198, 203, 208, 212, 217, 222, 227, 231, 236, 241, 246, 250, 255

Offset: 1

Author

Clark Kimberling, Nov 30 2010

Keywords

• nonn

Comments

Let u=2-sqrt(3) and v=1. Jointly rank {ju} and {kv} as in the first comment at A182760; a(n) is the position of n. A182778 is the complement of A182777.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A182760, A182777.

Programs

Magma

[Floor(n*(3+Sqrt(3))): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011

Mathematica

Table[Floor[(3+Sqrt[3])*n], {n, 54}]

Formula

a(n) = floor(n*(3 + sqrt(3))).

From Miko Labalan, Dec 17 2016: (Start)

a(n) = 3n + A022838(n);

For n > 0, a(n) = 5*floor(n*(sqrt(3)-1)) + 4*floor(n*(2-sqrt(3))) + 4;

a(0) = 0, a(n) = a(n - 1) + A022838(n) - A022838(n - 1) + 3.

(End)

Extensions

Typo in formula corrected by Vincenzo Librandi, Oct 25 2011