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Erdős problem 1102

There exists an infinite sequence A=a1<a2<SFA = {a₁ < a₂ < …} ⊂ \mathsf{SF} where SF:=Npp2N\mathsf{SF} := \mathbb{N} \setminus \bigcup_{p} p^{2}\mathbb{N}, i.e. the set of squarefree numbers. The set A has property Q and natural density 6 / π^2. Equivalently, (j / a_j) → 6/π^2 as j → ∞. -

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/1102.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1102.leanErdos1102.erdos_1102.density_zero_of_P2 linesExact file
∀ (A : ℕ → ℕ),  StrictMono AErdos1102.HasPropertyP (Set.range A) → Filter.Tendsto (fun j => ↑(A j) / ↑j) Filter.atTop Filter.atTop
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:1102
  • PLBY Lean proofsErdosProblems.Erdos1102

Reported activity

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

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