A276867 First differences of the Beatty sequence A003231 for 2 + tau, where tau = golden ratio = (1 + sqrt(5))/2.

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

Offset: 1

Author

Clark Kimberling, Sep 24 2016

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A003231, A276886.

Programs

Mathematica

z = 500; r = 2+GoldenRatio; b = Table[Floor[k*r], {k, 0, z}]; (* A003231 *)
Differences[b] (* A276867 *)

Formula

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