A276868 First differences of the Beatty sequence A276855 for 3 + tau, where tau = golden ratio = (1 + sqrt(5))/2.

4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 4, 5, 5, 4, 5, 4, 5, 5

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. A276855, A276887.

Programs

Mathematica

z = 500; r = 3+GoldenRatio; b = Table[Floor[k*r], {k, 0, z}]; (* A276855 *)
Differences[b] (* A276868 *)

Formula

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