A213911 Number of runs of consecutive zeros in the Zeckendorf (binary) representation of n.

0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 2, 2, 3, 3, 3, 3, 3, 4, 3, 3, 4

Offset: 0

Author

Reinhard Zumkeller, Mar 10 2013

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003849, A007895, A104324, A189920, A213676, A014417.

Programs

Haskell

import Data.List (group)
a213911 = length . filter ((== 0) . head) . group . a213676_row

Formula

a(n) = A104324(n) - A007895(n).

a(n) = A007895(n) - A003849(n). - Alexander Staunton, Jan 15 2025

Extensions

a(0)=0 added by N. J. A. Sloane, Jun 30 2017