erdős #348
For what values of is there a complete sequence of integers such that remains complete after removing any elements, but is not complete after removing any elements?
Open — best to date is a honest null, not yet sealed.
number theory · open · formalized (Lean) · 1 attempt
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vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
honest null
needs verification
attempted via frontier 'additive-basis' (transfer_strength=weak) -> no_progress
No solve/partial on this pass. Transfer into the owned frontier was 'weak'. Do not re-attack cold; needs a new idea or richer accumulated context.
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Let (A\subseteq \mathbb N) be written as a nondecreasing sequence (a_1\le a_2\le\cdots), and write [ P(A)=\\{\sum_{x\in B}x:;B\subseteq A\text{ finite}\\} ] for the set of finite subset sums. On the Erdős–Graham “complete sequence” convention, **$A$ is complete** if $P(A)$ contains **all sufficiently large** integers. …
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 11 · open (literature)
theorem erdos_348 :
{ (m, n) | (m) (n) (_ : m < n) (a : ℕ → ℕ) (_ : Monotone a)
(_ : ∀ s, s.card = m → IsAddComplete (Set.range (Function.updateFinset a s 0)))
(_ : ∀ t, t.card = n → ¬IsAddComplete (Set.range (Function.updateFinset a t 0))) } =
answer(sorry)formal-conjectures/348.lean ↗links
has shown · paper
status
open