Ruler sequence: a(n) = v₂(n) = exponent of 2 in factorization of n. a(1)=0, a(2)=1, a(3)=0, a(4)=2, a(5)=0, a(6)=1, a(7)=0, a(8)=3... Looks like ruler markings! Self-similar: between any two marks of height k, the pattern repeats. Equal to Tower of Hanoi move sequence.
How to Use
Enter number of terms:
- Sequence: v₂(n) values
- Visual: Ruler-like bars
- Binary: Trailing zeros
Tower of Hanoi
The optimal Hanoi solution: at step n, move disk a(n). The ruler sequence tells you which disk to move! Step 1: smallest (a(1)=0). Step 2: next (a(2)=1). Step 3: smallest again (a(3)=0). Step 4: third disk (a(4)=2).
Fractal Structure
The sequence is self-similar: between consecutive 1s, it's (0). Between consecutive 2s, it's (0,1,0). Between consecutive k's, the pattern of 0...(k-1) repeats. This is the same fractal structure as a physical ruler's markings.
Step-by-Step Instructions
- 1Enter terms.
- 2View sequence.
- 3See ruler bars.
- 4Check Hanoi.
- 5Analyze binary.