72200.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Smallest factorial containing exactly $n$ 6's

The sequence $a(n)$ gives the smallest $k$ such that the decimal expansion of $k!$ contains exactly $n$ occurrences of the digit '6', or $0$ if no such $k$ exists.

References:

A072200

Imports (1)

FormalConjecturesUtil

def OeisA72200.a Smallest $k$ such that $k!$ contains exactly $n$ 6's in base 10, or 0 if no such $k$ exists line 36 source
Source documentation
Smallest $k$ such that $k!$ contains exactly $n$ 6's in base 10, or 0 if no such $k$ exists.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: dite, Exists, Eq, List.count, OfNat.ofNat, Nat.digits, Nat.factorial, Classical.propDecidable, Nat.find, Not
3 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
theorem OeisA72200.a_1 Value of the sequence a at 1 line 44 source
Source documentation
Value of the sequence a at 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA72200.a, OfNat.ofNat
Proof uses: id, dite, Exists, List.count, Nat.digits, Nat.factorial, Classical.propDecidable, Nat.find, Not, Eq.mpr, congrFun', congrArg, dif_pos, And, LT.lt, propext, Nat.find_eq_iff, of_decide_eq_true, Bool, Decidable.decide and 10 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 3 := by
…
```
Mentions: OeisA72200.a
theorem OeisA72200.a_2 Value of the sequence a at 2 line 54 source
Source documentation
Value of the sequence a at 2.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA72200.a, OfNat.ofNat
Proof uses: id, dite, Exists, List.count, Nat.digits, Nat.factorial, Classical.propDecidable, Nat.find, Not, Eq.mpr, congrFun', congrArg, dif_pos, And, LT.lt, propext, Nat.find_eq_iff, of_decide_eq_true, Bool, Decidable.decide and 10 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
theorem a_2 : a 2 = 15 := by
…
```
Mentions: OeisA72200.a
theorem OeisA72200.a_3 Value of the sequence a at 3 line 64 source
Source documentation
Value of the sequence a at 3.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA72200.a, OfNat.ofNat
Proof uses: id, dite, Exists, List.count, Nat.digits, Nat.factorial, Classical.propDecidable, Nat.find, Not, Eq.mpr, congrFun', congrArg, dif_pos, And, LT.lt, propext, Nat.find_eq_iff, of_decide_eq_true, Bool, Decidable.decide and 10 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : a 3 = 23 := by
…
```
Mentions: OeisA72200.a
theorem OeisA72200.a_4 Value of the sequence a at 4 line 74 source
Source documentation
Value of the sequence a at 4.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA72200.a, OfNat.ofNat
Proof uses: id, dite, Exists, List.count, Nat.digits, Nat.factorial, Classical.propDecidable, Nat.find, Not, Eq.mpr, congrFun', congrArg, dif_pos, And, LT.lt, propext, Nat.find_eq_iff, of_decide_eq_true, Bool, Decidable.decide and 10 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
theorem a_4 : a 4 = 26 := by
…
```
Mentions: OeisA72200.a
theorem OeisA72200.a_5 Value of the sequence a at 5 line 84 source
Source documentation
Value of the sequence a at 5.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA72200.a, OfNat.ofNat
Proof uses: id, dite, Exists, List.count, Nat.digits, Nat.factorial, Classical.propDecidable, Nat.find, Not, Eq.mpr, congrFun', congrArg, dif_pos, And, LT.lt, propext, Nat.find_eq_iff, of_decide_eq_true, Bool, Decidable.decide and 10 more
8 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
theorem a_5 : a 5 = 32 := by
…
```
Mentions: OeisA72200.a
theorem OeisA72200.conjecture It is conjectured that $a(24) = 0$ since no factorial less than $10000$ contained just 24 sixes sorry line 95 source
Source documentation
It is conjectured that $a(24) = 0$ since no factorial less than $10000$ contained just 24 sixes.

depends on sorry what this means
Statement uses: Eq, Nat, OeisA72200.a, 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 : a 24 = 0 := by
…
```
Mentions: OeisA72200.a