A133775 - OEIS

%I #18 Apr 21 2023 07:58:11

%S 0,2,3,2,5,5,7,6,5,5,4,8,8,8,7,8,8,11,10,9,9,8,8,8,9,8,7,7,6,11,11,11,

%T 10,11,11,12,11,10,10,9,11,11,11,10,11,11,15,14,13,13,12,12,12,13,12,

%U 11,11,10,11,11,11,10,11,11,13,12,11,11,10,10,10,11,10,9,9,8,14,14,14,13,14,14

%N Number of 0's in the minimal "phinary" (A130600) representation of n.

%D Zeckendorf, E., Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41, 179-182, 1972.

%H Casey Mongoven and T. D. Noe, <a href="/A133775/b133775.txt">Table of n, a(n) for n = 1..1000</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phigits.html">Using Powers of Phi to represent Integers</a>.

%F For n > 1, a(n) <= A190796(n) - 2. - _Charles R Greathouse IV_, Apr 21 2023

%e A130600(5)=10001001, which has five 0's. So a(5)=5.

%t nn = 100; len = 2*Ceiling[Log[GoldenRatio, nn]]; Table[d = RealDigits[n, GoldenRatio, len]; last1 = Position[d[[1]], 1][[-1, 1]]; Count[Take[d[[1]], last1], 0], {n, 1, nn}] (* _T. D. Noe_, May 20 2011 *)

%Y Cf. A133776, A130600.

%K nonn

%O 1,2

%A _Casey Mongoven_, Sep 23 2007