A133772 Number of runs (of equal bits) in the minimal "phinary" (A130600) representation of n.

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

Offset: 1

Author

Casey Mongoven, Sep 23 2007

Keywords

• nonn

Examples

			A130600(3)=10001 because phi^2 + phi^-2 = 3; 10001 has 3 runs: 1,000,1. So a(3)=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.

Crossrefs

Cf. A133773, A130600.