A184618 a(n) = floor(n*r + h), where r=sqrt(2) and h=1/3; complement of A184619.

1, 3, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 28, 30, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 71, 72, 73, 75, 76, 78, 79, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 97

Offset: 1

Author

Clark Kimberling, Jan 18 2011

Keywords

• nonn

Comments

Sequences of the form (floor(n*r + h)) are sometimes called nonhomogeneous Beatty sequences when h is not zero.

Links

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

Crossrefs

Cf. A184619.

Programs

Magma

[Floor(n*Sqrt(2)+1/3): n in [1..80]]; // Vincenzo Librandi, Jul 07 2011

Mathematica

r=2^(1/2); h=1/3; s=r/(r-1);
Table[Floor[n*r+h],{n,1,120}]  (* A184618 *)
Table[Floor[n*s+h-h*s],{n,1,120}]  (* A184619 *)

PARI

a(n)=floor(n*sqrt(2)+1/3) \\ Charles R Greathouse IV, Jul 07 2011

Formula

a(n) = floor(n*r + h), where r=sqrt(2), h=1/3.