FormalConjectures/OEIS/228828.lean

GitHub source file

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL
Lean4 Domain Explanation Language

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

5 declarations, 1 contain sorry, 0 declared as axioms

Numbers $n$ such that $n^2 + \pi(n)$ is prime

References:

Imports (1)
Imported by 1 file
  1. def OeisA228828.a Numbers $n$ such that $n^2 + \pi(n)$ is prime line 36 source

    Source documentation

    Numbers $n$ such that $n^2 + \pi(n)$ is prime.

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Nat

    Proof uses: Nat.nth, Nat.Prime, HAdd.hAdd, HPow.hPow, OfNat.ofNat, Nat.primeCounting

    7 instances, coercions and auxiliary constants left out.

    noncomputable def a (n : ℕ) : ℕ := n.nth (fun n => (n ^ 2 + π n).Prime)
…
  2. theorem OeisA228828.a_0 line 39 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA228828.a, OfNat.ofNat

    Proof uses: id, Eq.mpr, Nat.nth, Nat.Prime, HAdd.hAdd, HPow.hPow, Nat.primeCounting, Nat.count, Classical.decPred, eq_of_heq, HEq, Eq.refl, HEq.refl, Eq.symm, of_eq_true, Eq.trans, True, congrArg, ite, Nat.count_succ and 23 more

    18 instances, coercions and auxiliary constants left out.

    Tactic trace: 8 steps

    Open to load the checked before-and-after goal states.

  3. theorem OeisA228828.a_1 line 47 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA228828.a, OfNat.ofNat

    Proof uses: id, Eq.mpr, Nat.nth, Nat.Prime, HAdd.hAdd, HPow.hPow, Nat.primeCounting, Nat.count, Classical.decPred, eq_of_heq, HEq, Eq.refl, HEq.refl, Eq.symm, Eq.trans, Not, ite, congrArg, Nat.count_succ, congr and 25 more

    22 instances, coercions and auxiliary constants left out.

    Tactic trace: 9 steps

    Open to load the checked before-and-after goal states.

  4. theorem OeisA228828.a_2 line 56 source

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Eq, Nat, OeisA228828.a, OfNat.ofNat

    Proof uses: id, Eq.mpr, Nat.nth, Nat.Prime, HAdd.hAdd, HPow.hPow, Nat.primeCounting, Nat.count, Classical.decPred, eq_of_heq, HEq, Eq.refl, HEq.refl, Eq.symm, ite, congrArg, Eq.trans, Nat.count_succ, congr, Nat.count_zero and 22 more

    18 instances, coercions and auxiliary constants left out.

    Tactic trace: 9 steps

    Open to load the checked before-and-after goal states.

  5. theorem OeisA228828.conjecture Conjecture: the sequence A228828 is infinite sorry line 68 source

    Source documentation

    Conjecture: the sequence A228828 is infinite.

    depends on sorry what this means

    Statement uses: Set.Infinite, Nat, Set.ofPred, Exists, Eq, OeisA228828.a

    Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat

    1 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

    theorem conjecture : {a n | n}.Infinite := by
…

    Mentions: OeisA228828.a