Let $n_1<n_2<\cdots$ be the sequence of integers which are the sum of two squares. Explore the behaviour of (i.e. find good upper and lower bounds for) the consecutive differences $n_{k+1}-n_k$.

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

Let [ \mathcal S={n\ge 0:\ n=a^2+b^2\text{ for some }a,b\in\mathbb Z},\qquad n_1<n_2<\cdots ] be the increasing enumeration of (\mathcal S), and set the gaps [ g_k:=n_{k+1}-n_k,\qquad g(X):=\max_{n_{k+1}\le X}(n_{k+1}-n_k). ]

llm-hunter · gpt pro 5.2 · unverified

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