Erdős problem 1102 · problems.science

There exists an infinite sequence $A = {a₁ < a₂ < …} ⊂ \mathsf{SF}$ where $\mathsf{SF} := \mathbb{N} \setminus \bigcup_{p} p^{2}\mathbb{N}$ , 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 → ∞. -

Sources

Browse retained paths and inspect the exact material available for this Problem.

4 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

1102.lean

Retained formal statement4 of 4

Every sequence with property Q has upper density at most 6 / π^2. -

FormalConjectures/ErdosProblems/1102.leanErdos1102.erdos_1102.upper_density_Q3 linesExact file

1∀ (A : ℕ → ℕ),2  StrictMono A →3    Erdos1102.HasPropertyQ (Set.range A) → Filter.limsup (fun j => ↑j / ↑(A j)) Filter.atTop ≤ 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.

Sources

Search problems.science