A133770 Number of runs (of equal bits) in the minimal Lucas binary (A130310) representation of n.
2, 1, 2, 2, 4, 3, 2, 4, 3, 4, 2, 4, 3, 4, 4, 6, 5, 2, 4, 3, 4, 4, 6, 5, 4, 6, 5, 6, 2, 4, 3, 4, 4, 6, 5, 4, 6, 5, 6, 4, 6, 5, 6, 6, 8, 7, 2, 4, 3, 4, 4, 6, 5, 4, 6, 5, 6, 4, 6, 5, 6, 6, 8, 7, 4, 6, 5, 6, 6, 8, 7, 6, 8, 7, 8, 2, 4, 3, 4, 4, 6, 5, 4, 6, 5, 6, 4, 6, 5, 6, 6, 8, 7, 4, 6, 5, 6, 6, 8, 7, 6, 8, 7, 8, 4
Offset: 1
Keywords
Examples
A130310(17)=101001 because 11 + 4 + 2 = 17 (a sum of Lucas numbers); this representation has five runs: 1,0,1,00,1. So a(17)=5.
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.