70823.lean`

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

9 declarations, 1 contain sorry, 0 declared as axioms

Recurrence $a(n+2) = |a(n+1)a(n) - a(n)a(n+1)|$ via concatenation

The sequence starts with $a(1) = 0, a(2) = 1$. For $n \ge 1$, $$a(n+2) = |\text{concat}(a(n+1), a(n)) - \text{concat}(a(n), a(n+1))|$$ where concatenation is in decimal representation.

References:

A070823

Imports (1)

FormalConjecturesUtil

def OeisA70823.numDigitsBase10 Number of digits of a natural number $n$ in base 10 (with 1 digit for 0) line 36 source
Source documentation
Number of digits of a natural number $n$ in base 10 (with 1 digit for 0).

no axioms what this means
Statement uses: Nat
Proof uses: ite, Eq, OfNat.ofNat, HAdd.hAdd, Nat.log
4 instances, coercions and auxiliary constants left out.
```
def numDigitsBase10 (n : ℕ) : ℕ :=
…
```
def OeisA70823.concatenate Concatenate $x$ followed by $y$ in base 10 line 40 source
Source documentation
Concatenate $x$ followed by $y$ in base 10.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: HAdd.hAdd, HMul.hMul, HPow.hPow, OfNat.ofNat, OeisA70823.numDigitsBase10
9 instances, coercions and auxiliary constants left out.
```
def concatenate (x y : ℕ) : ℕ :=
…
```
def OeisA70823.a The sequence $a(1)=0, a(2)=1, a(n+2)=|\text{concat}(a(n+1),a(n))-\text{concat}(a(n),a(n+1))|$ line 44 source
Source documentation
The sequence $a(1)=0, a(2)=1, a(n+2)=|\text{concat}(a(n+1),a(n))-\text{concat}(a(n),a(n+1))|$.

standard axioms: propext what this means
Statement uses: Nat
2 instances, coercions and auxiliary constants left out.
```
def a : ℕ → ℕ
  | 0 => 0
  | 1 => 0
  | 2 => 1
  | n + 3 =>
    let cat1 := concatenate (a (n + 2)) (a (n + 1))
…
```
Mentions: OeisA70823.concatenate
theorem OeisA70823.a_1 Value of the sequence a at 1 line 55 source
Source documentation
Value of the sequence a at 1.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA70823.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.
```
theorem a_1 : a 1 = 0 := by
…
```
Mentions: OeisA70823.a
theorem OeisA70823.a_2 Value of the sequence a at 2 line 60 source
Source documentation
Value of the sequence a at 2.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA70823.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.
```
theorem a_2 : a 2 = 1 := by
…
```
Mentions: OeisA70823.a
theorem OeisA70823.a_3 Value of the sequence a at 3 line 65 source
Source documentation
Value of the sequence a at 3.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA70823.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.
```
theorem a_3 : a 3 = 9 := by
…
```
Mentions: OeisA70823.a
theorem OeisA70823.a_4 Value of the sequence a at 4 line 70 source
Source documentation
Value of the sequence a at 4.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA70823.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.
```
theorem a_4 : a 4 = 72 := by
…
```
Mentions: OeisA70823.a
theorem OeisA70823.a_5 Value of the sequence a at 5 line 75 source
Source documentation
Value of the sequence a at 5.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA70823.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.
```
theorem a_5 : a 5 = 243 := by
…
```
Mentions: OeisA70823.a
theorem OeisA70823.conjecture sorry line 87 source
depends on sorry what this means
Statement uses: Iff, False, Nat, LT.lt, OfNat.ofNat, And, Nat.ModEq, OeisA70823.a, Exists, Eq, HMul.hMul, HPow.hPow, Squarefree
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.