Hofstadter Q-sequence: Q(1)=Q(2)=1, Q(n)=Q(n−Q(n−1)). From Gödel, Escher, Bach. Behaves chaotically yet Q(n)/n→1. The R-sequence uses a different self-reference. These meta-Fibonacci sequences are notoriously difficult to analyze.
How to Use
Enter n:
- Q(n): Hofstadter Q value
- Sequence: First n terms
- Ratio: Q(n)/n convergence
Chaotic Behavior
Q(n) is extremely erratic: no known closed form, no proven growth rate, no proof it's even defined for all n (conjectured). Q(n)/n appears to converge to 1 but this is unproven. Consecutive differences are unbounded.
Hofstadter Variants
- Q: Q(n) = Q(n−Q(n−1))
- R: R(n) = R(n−R(n−1)) + R(n−R(n−2))
- Male/Female: mutual recursion
- Figure-Ground: based on complement
Step-by-Step Instructions
- 1Choose sequence type.
- 2Enter n.
- 3View terms.
- 4Analyze ratio.
- 5Compare variants.