FormalConjectures/OEIS/116150.lean

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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

7 declarations, 1 contain sorry, 0 declared as axioms

$a(n) = \sum_{j=1}^{n} (3^j + (-2)^j)$

References:

Imports (1)
  1. def OeisA116150.a a n is the sum of $3^j + (-2)^j$ for j from 1 to n line 34 source

    Source documentation

    a n is the sum of $3^j + (-2)^j$ for j from 1 to n.

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

    Statement uses: Nat

    Proof uses: Int.toNat, Finset.sum, Int, Finset.Icc, OfNat.ofNat, HAdd.hAdd, HPow.hPow, Neg.neg

    12 instances, coercions and auxiliary constants left out.

    def a (n : ℕ) : ℕ :=
…
  2. theorem OeisA116150.a_1 line 38 source

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

    Statement uses: Eq, Nat, OeisA116150.a, OfNat.ofNat

    Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl

    3 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  3. theorem OeisA116150.a_2 line 41 source

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

    Statement uses: Eq, Nat, OeisA116150.a, OfNat.ofNat

    Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl

    3 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  4. theorem OeisA116150.a_3 line 44 source

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

    Statement uses: Eq, Nat, OeisA116150.a, OfNat.ofNat

    Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl

    3 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  5. theorem OeisA116150.a_4 line 47 source

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

    Statement uses: Eq, Nat, OeisA116150.a, OfNat.ofNat

    Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl

    3 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  6. theorem OeisA116150.a_5 line 50 source

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

    Statement uses: Eq, Nat, OeisA116150.a, OfNat.ofNat

    Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl

    3 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  7. theorem OeisA116150.conjecture First primes are $a(11) = 264353$ and $a(17) = 193622861$ sorry line 58 source

    Source documentation

    First primes are $a(11) = 264353$ and $a(17) = 193622861$. Additional primes: $a(71)$, $a(91)$, $a(431)$. What is the next prime?

    depends on sorry what this means

    Statement uses: Eq, Nat, sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, OeisA116150.a, InfSet.sInf, Set.ofPred, And, LT.lt, Nat.Prime

    6 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

    theorem conjecture : answer(sorry) = a (sInf {n : ℕ | 431 < n ∧ (a n).Prime}) := by
…

    Mentions: OeisA116150.a