A276870 First differences of the Beatty sequence A110117 for sqrt(2) + sqrt(3).

3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3

Offset: 1

Author

Clark Kimberling, Sep 26 2016

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A110117, A276889.

Programs

Magma

[Floor(n*(Sqrt(2) + Sqrt(3))) - Floor((n-1)*(Sqrt(2) + Sqrt(3))): n in [1..100]]; // G. C. Greubel, Aug 16 2018

Mathematica

z = 500; r = Sqrt[2]+Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}] (* A110117 *)
Differences[b] (* A276870 *)

PARI

vector(100, n, floor(n*(sqrt(2) + sqrt(3))) - floor((n-1)*(sqrt(2)+sqrt(3)))) \\ G. C. Greubel, Aug 16 2018

Formula

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