Skip to content

Erdős problem 347

Is there a sequence A={a1≤a2≤⋯ }A=\{a_1\leq a_2\leq \cdots\} of integers with lim⁡an+1an=2\lim \frac{a_{n+1}}{a_n}=2 such that P(A′)={∑n∈Bn:B⊆A′ finite }P(A')= \left\{\sum_{n\in B}n : B\subseteq A'\textrm{ finite }\right\} has density 11 for every cofinite subsequence A′A' of AA?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/347.lean

Formal Conjectures

FormalConjectures/ErdosProblems/347.leanErdos347.erdos_3475 linesExact file
True ↔  ∃ a,    Monotone a ∧      Filter.Tendsto (fun n => ↑(a (n + 1)) / ↑(a n)) Filter.atTop (nhds 2) ∧        ∀ (ι : ℕ → ℕ), (Set.range ι)ᶜ.Finite → (subsetSums (Set.range (a ∘ ι))).HasDensity 1
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:347
  • PLBY Lean proofsErdosProblems.Erdos347

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • AI collaborating with humans

    Erdős AI contributions wiki · 25 Oct, 2025-4 Feb, 2026

    Machine
    Aristotle, Claude Opus, Codex, GPT
    People
    Enrique Barschkis, Wouter van Doorn, jbbaehr22, Bartosz Naskrecki, Terence Tao
    Open the source record

  • argument

    VibeMathed

    Machine
    Aristotle, Claude Opus, Codex, GPT
    People
    Enrique Barschkis, Wouter van Doorn, jbbaehr22, Bartosz Naskrecki, Terence Tao
    Reported outcome
    resolved
    Open the source record

Continue

Start a contributionBrowse the source filesOpen the collection entry

Search problems.science

Find a Problem, Result, source, or page