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A133775 Number of 0s in the minimal "phinary" (A130600) representation of n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Zeckendorf, E., Repr├ęsentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Li├Ęge 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.

EXAMPLE

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

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)