A133773 Number of runs (of equal bits) in the maximal "phinary" (A130601) representation of n.

1, 1, 3, 5, 3, 3, 7, 5, 5, 5, 9, 5, 5, 7, 5, 5, 5, 11, 9, 9, 7, 5, 7, 7, 9, 7, 7, 7, 13, 7, 7, 9, 7, 7, 7, 11, 9, 9, 7, 5, 7, 7, 9, 7, 7, 7, 15, 13, 13, 11, 9, 11, 11, 11, 9, 9, 7, 5, 9, 9, 11, 9, 9, 9, 13, 11, 11, 9, 7, 9, 9, 11, 9, 9, 9, 17, 9, 9, 11, 9, 9, 9, 13, 11, 11, 9, 7, 9, 9, 11, 9, 9, 9, 15, 13

Offset

1,3

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, Table of n, a(n) for n = 1..199

Ron Knott, Using Powers of Phi to represent Integers.

Casey Mongoven, Music based on this sequence.

Example

A130601(3)=1101 because phi^1 + phi^0 + phi^-2 = 3; 1101 has 3 runs: 11,0,1. So a(3)=3.

Crossrefs

Cf. A133772, A130601.

Sequence in context: A073703 A175019 A097519 * A327555 A346915 A077934

Adjacent sequences: A133770 A133771 A133772 * A133774 A133775 A133776

Keyword

nonn

Author

Casey Mongoven, Sep 23 2007

Status

approved