A182769 Beatty sequence for (4 + sqrt(2))/2.

2, 5, 8, 10, 13, 16, 18, 21, 24, 27, 29, 32, 35, 37, 40, 43, 46, 48, 51, 54, 56, 59, 62, 64, 67, 70, 73, 75, 78, 81, 83, 86, 89, 92, 94, 97, 100, 102, 105, 108, 110, 113, 116, 119, 121, 124, 127, 129, 132, 135, 138, 140, 143, 146, 148, 151, 154, 157, 159, 162, 165, 167, 170, 173, 175

Offset: 1

Author

Clark Kimberling, Nov 30 2010

Keywords

• nonn

Comments

Let u=1+sqrt(2) and v=sqrt(2). Jointly rank {j*u} and {k*v} as in the first comment at A182760; a(n) is the position of n*u.

Is this a shifted version of A126281? - R. J. Mathar, Jan 24 2011

The answer to R. J. Mathar's question is no: A126281 contains 65 while this sequence does not. - L. Edson Jeffery, Sep 02 2014

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A182760, A182770.

Programs

Magma

[Floor(n*(4 + Sqrt(2))/2): n in [1..50]]; // G. C. Greubel, Jan 27 2018

Mathematica

Table[Floor[n*(4 + Sqrt[2])/2], {n, 1, 100}] (* G. C. Greubel, Jan 27 2018 *)

PARI

a(n) = floor(n*(4+sqrt(2))/2); \\ Michel Marcus, Sep 02 2014

Formula

a(n) = floor(n*(4 + sqrt(2))/2).