FormalConjectures/OEIS/113258.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

6 declarations, 1 contain sorry, 0 declared as axioms

Ascending descending base exponent transform of factorials

References:

Imports (1)
  1. def OeisA113258.a The primary defining sequence a line 38 source

    Source documentation

    The primary defining sequence a. $a(n)$ is the ascending descending base exponent transform of factorials. $$a(n) = \sum_{i = 1}^n (i!) ^ {(n-i+1)!}$$

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

    Statement uses: Nat

    Proof uses: Finset.sum, Finset.range, HPow.hPow, Nat.factorial, HAdd.hAdd, OfNat.ofNat, HSub.hSub

    10 instances, coercions and auxiliary constants left out.

    def a (n : ℕ) : ℕ :=
…
  2. theorem OeisA113258.a_1 line 42 source

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

    Statement uses: Eq, Nat, OeisA113258.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  3. theorem OeisA113258.a_2 line 45 source

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

    Statement uses: Eq, Nat, OeisA113258.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  4. theorem OeisA113258.a_3 line 48 source

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

    Statement uses: Eq, Nat, OeisA113258.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  5. theorem OeisA113258.a_4 line 51 source

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

    Statement uses: Eq, Nat, OeisA113258.a, OfNat.ofNat

    Proof uses: Eq.refl

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

  6. theorem OeisA113258.conjecture Is there a nontrivial power after $a(4) = 5^3$? sorry line 57 source

    Source documentation

    Is there a nontrivial power after $a(4) = 5^3$?

    depends on sorry what this means

    Statement uses: Iff, True, Exists, Nat, And, GT.gt, OfNat.ofNat, Eq, OeisA113258.a, HPow.hPow

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

    12 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) ↔ ∃ n > 4, ∃ b > 1, ∃ e > 1, a n = b ^ e := by
…

    Mentions: OeisA113258.a