FormalConjectures/OEIS/113010.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

Number of digits of n raised to the power of the sum of the digits of n

References:

Imports (1)
  1. def OeisA113010.a a n is the {Number of digits of n} raised to the power of {the sum of the digits of n} line 37 source

    Source documentation

    a n is the {Number of digits of n} raised to the power of {the sum of the digits of n}.

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

    Statement uses: Nat

    Proof uses: HPow.hPow, List.length, Nat.digits, OfNat.ofNat, List.sum

    8 instances, coercions and auxiliary constants left out.

    def a (n : ℕ) : ℕ :=
…
  2. theorem OeisA113010.a_0 line 41 source

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

    Statement uses: Eq, Nat, OeisA113010.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 OeisA113010.a_1 line 44 source

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

    Statement uses: Eq, Nat, OeisA113010.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 OeisA113010.a_2 line 47 source

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

    Statement uses: Eq, Nat, OeisA113010.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 OeisA113010.a_3 line 50 source

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

    Statement uses: Eq, Nat, OeisA113010.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 OeisA113010.a_4 line 53 source

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

    Statement uses: Eq, Nat, OeisA113010.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 OeisA113010.conjecture $n=1$ and $32$ are two fixed points sorry line 59 source

    Source documentation

    $n=1$ and $32$ are two fixed points. Are there any others?

    depends on sorry what this means

    Statement uses: Iff, True, Exists, Nat, And, Eq, OeisA113010.a, Ne, OfNat.ofNat

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

    2 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 : ℕ, a n = n ∧ n ≠ 1 ∧ n ≠ 32 := by
…

    Mentions: OeisA113010.a