A133771 Number of runs (of equal bits) in the maximal Lucas binary (A130311) representation of n.

2, 1, 1, 2, 3, 1, 3, 2, 3, 1, 4, 5, 3, 3, 2, 3, 1, 5, 4, 5, 3, 4, 5, 3, 3, 2, 3, 1, 6, 7, 5, 5, 4, 5, 3, 5, 4, 5, 3, 4, 5, 3, 3, 2, 3, 1, 7, 6, 7, 5, 6, 7, 5, 5, 4, 5, 3, 6, 7, 5, 5, 4, 5, 3, 5, 4, 5, 3, 4, 5, 3, 3, 2, 3, 1, 8, 9, 7, 7, 6, 7, 5, 7, 6, 7, 5, 6, 7, 5, 5, 4, 5, 3, 7, 6, 7, 5, 6, 7, 5, 5, 4, 5, 3, 6

Offset

1,1

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

Table of n, a(n) for n=1..105.

Ron Knott, Using Powers of Phi to represent Integers.

Example

A130311(19)=101110 because 11+4+3+1=19 (a sum of Lucas numbers); this representation has four runs: 1,0,111,0. So a(19)=4.

Crossrefs

Cf. A133770, A130311.

Sequence in context: A182972 A153452 A090680 * A352895 A288158 A319522

Adjacent sequences: A133768 A133769 A133770 * A133772 A133773 A133774

Keyword

nonn

Author

Casey Mongoven, Sep 23 2007; corrected Mar 23 2008

Extensions

The b-file submitted by Casey Mongoven did not match the terms of the sequence, so I have deleted it. Of course it may be that the sequence is wrong and the b-file was correct. Should be rechecked. - N. J. A. Sloane, Nov 10 2010

Status

approved