109671.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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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

Conjectures associated with A109671

$a(1)=1$; thereafter, $a(2n)=a(n)$, $a(2n+1)$ is the smallest positive number such that $|a(2n+1)-a(2n-1)|=a(n)$. Conjecture: Does the sequence contain every positive integer?

References:

A109671

Imports (1)

FormalConjecturesUtil

def OeisA109671.a The primary defining sequence a line 40 source
Source documentation
The primary defining sequence a. $a(1)=1$; thereafter, $a(2n)=a(n)$, $a(2n+1)$ is the smallest positive number such that $|a(2n+1)-a(2n-1)|=a(n)$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: WellFounded.Nat.fix, InvImage, LT.lt, dite, Eq, OfNat.ofNat, Not, HMod.hMod, HDiv.hDiv, HSub.hSub, GT.gt, HAdd.hAdd
15 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA109671.a_1 line 56 source
extra axioms: _private.0.OeisA109671.a_1._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA109671.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA109671.a_2 line 59 source
extra axioms: _private.0.OeisA109671.a_2._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA109671.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA109671.a_3 line 62 source
extra axioms: _private.0.OeisA109671.a_3._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA109671.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA109671.a_4 line 65 source
extra axioms: _private.0.OeisA109671.a_4._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA109671.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA109671.a_5 line 68 source
extra axioms: _private.0.OeisA109671.a_5._native.native_decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA109671.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA109671.conjecture Does the sequence contain every positive integer (cf. A169741)? sorry line 74 source
Source documentation
Does the sequence contain every positive integer (cf. A169741)?

depends on sorry what this means
Statement uses: Iff, True, Nat, LT.lt, OfNat.ofNat, Exists, And, Eq, OeisA109671.a
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
4 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) ↔ ∀ m : ℕ, 0 < m → ∃ n : ℕ, 0 < n ∧ a n = m := by
…
```
Mentions: OeisA109671.a