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
Keywords
Examples
A130601(3)=1101 because phi^1 + phi^0 + phi^-2 = 3; 1101 has 3 runs: 11,0,1. 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.
- Casey Mongoven, Music based on this sequence.