A133775 Number of 0's in the minimal "phinary" (A130600) representation of n.

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

Offset

1,2

References

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.

Links

Casey Mongoven and T. D. Noe, Table of n, a(n) for n = 1..1000

Ron Knott, Using Powers of Phi to represent Integers.

Formula

For n > 1, a(n) <= A190796(n) - 2. - Charles R Greathouse IV, Apr 21 2023

Example

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

Mathematica

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 *)

Crossrefs

Cf. A133776, A130600.

Sequence in context: A074196 A153023 A068319 * A099043 A318677 A239327

Adjacent sequences: A133772 A133773 A133774 * A133776 A133777 A133778

Keyword

nonn

Author

Casey Mongoven, Sep 23 2007

Status

approved