Let $a_{1} = 2$ and $a_{2} = 3$ and continue the sequence by appending to $a_{1}, \dots, a_{n}$ all possible values of $a_{i} a_{j} - 1$ with $i \neq = j$ . Is it true that the set of integers which eventually appear has positive density?

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

This is a well-known open problem (asked by Hofstadter and recorded as **Erdős Problem #424**). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_424 : answer(sorry) ↔ generatedSet.HasPosDensity

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