Is there $A\subseteq \mathbb{N}$ such that$$\underset{n\to \infty }{\lim }\frac{1_A\ast 1_A(n)}{\log n}$$exists and is $\ne 0$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Write [ r_A(n):=(1_A*1_A)(n)=\sum_{k=0}^n 1_A(k),1_A(n-k), ] so (r_A(n)) is the **number of ordered representations** (n=a+b) with (a,b\in A) (up to an $O(1)$ difference from the unordered version).

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

3 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.