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

1,1

Links

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

Formula

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

Mathematica

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

Crossrefs

Cf. A003231, A276886.

Sequence in context: A066783 A046536 A052384 * A100867 A220196 A128200

Adjacent sequences: A276864 A276865 A276866 * A276868 A276869 A276870

Keyword

nonn,easy

Author

Clark Kimberling, Sep 24 2016

Status

approved