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Erdős problem 1102

There exists an infinite sequence A=a1<a2<…⊂SFA = {a₁ < a₂ < …} ⊂ \mathsf{SF} where SF:=N∖⋃pp2N\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 → ∞. -

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1102.lean

Retained formal statement3 of 4

There exists an infinite sequence A=a1<a2<…⊂SFA = {a₁ < a₂ < …} ⊂ \mathsf{SF} where SF:=N∖⋃pp2N\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 → ∞. -

FormalConjectures/ErdosProblems/1102.leanErdos1102.erdos_1102.lower_density_Q_exists4 linesExact file
∃ A,  StrictMono A ∧    (∀ (j : ℕ), Squarefree (A j)) ∧      Erdos1102.HasPropertyQ (Set.range A) ∧ Filter.Tendsto (fun j => ↑j / ↑(A j)) Filter.atTop (nhds (6 / Real.pi ^ 2))
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.

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