A081117 Differences of Beatty sequence for cube root of 2.

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1

Offset

0,4

Links

Zhuorui He, Table of n, a(n) for n = 0..10000

Formula

a(n) = floor((n+1)*2^(1/3)) - floor(n*2^(1/3)).

Mathematica

With[{c=Surd[2, 3]}, Differences[Floor[Range[0, 110]c]]] (* Harvey P. Dale, Jan 30 2015 *)

Prog

(PARI) a(n)=sqrtnint((n+1)^3*2, 3)-sqrtnint(n^3*2, 3);

Crossrefs

First differences of A038129.

Cf. A002580.

Sequence in context: A069291 A364209 A268238 * A368334 A129252 A327936

Adjacent sequences: A081114 A081115 A081116 * A081118 A081119 A081120

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 16 2003

Status

approved