Seminar Details

Hofstadter's Q-sequence is defined by Q(1) = Q(2) = 1 and Q(n) = Q(n - Q(n-1)) + Q(n - Q(n-2)). Its erratic behavior has so far defeated attempts to prove basic properties, such as its well-definedness for all n. In 2026, Marco Mantovanelli introduced an alternating perturbation, yielding the more stable variant Q*. Recent work proves its well-definedness, describes its dyadic and combinatorial structure, and establishes that Q*(n)/n ->1/2. I will outline these results and then return to Q, explaining how Q* can serve as a stable proxy in addressing the question of its well-definedness. I will also describe the AI-assisted methodology behind this work. Many recent AI successes in mathematics begin with an established framework. For example, by improving a bound, finding a counterexample, or linking disparate results from different fields. Here, by contrast, there was no ready-made framework for relating Q and Q*: the strategy itself had to be developed experimentally with human insight.