78590.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

$a(1)=1, a(2)=1, a(n)=(2^{a(n-1)} + 1)/a(n-2)$

The sequence is defined by $a(1) = 1, a(2) = 1$, and for $n \ge 3$, $$a(n) = \frac{2^{a(n-1)} + 1}{a(n-2)}$$

References:

A078590

Imports (1)

FormalConjecturesUtil

def OeisA78590.a $a(1)=1, a(2)=1, a(n)=(2^{a(n-1)} + 1)/a(n-2)$ line 34 source
Source documentation
$a(1)=1, a(2)=1, a(n)=(2^{a(n-1)} + 1)/a(n-2)$.

standard axioms: propext what this means
Statement uses: Nat
2 instances, coercions and auxiliary constants left out.
```
def a : ℕ → ℕ
  | 0 => 0
  | 1 => 1
  | 2 => 1
  | n + 3 => (2 ^ a (n + 2) + 1) / a (n + 1)

/-- Value of the sequence `a` at 1. -/
@[category test, AMS 11]
```
Mentions: test, AMS
theorem OeisA78590.a_1 Value of the sequence a at 1 line 42 source
Source documentation
Value of the sequence a at 1.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA78590.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.
```
theorem a_1 : a 1 = 1 := by
…
```
Mentions: OeisA78590.a
theorem OeisA78590.a_2 Value of the sequence a at 2 line 47 source
Source documentation
Value of the sequence a at 2.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA78590.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.
```
theorem a_2 : a 2 = 1 := by
…
```
Mentions: OeisA78590.a
theorem OeisA78590.a_3 Value of the sequence a at 3 line 52 source
Source documentation
Value of the sequence a at 3.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA78590.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.
```
theorem a_3 : a 3 = 3 := by
…
```
Mentions: OeisA78590.a
theorem OeisA78590.a_4 Value of the sequence a at 4 line 57 source
Source documentation
Value of the sequence a at 4.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA78590.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.
```
theorem a_4 : a 4 = 9 := by
…
```
Mentions: OeisA78590.a
theorem OeisA78590.a_5 Value of the sequence a at 5 line 62 source
Source documentation
Value of the sequence a at 5.

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA78590.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.
```
theorem a_5 : a 5 = 171 := by
…
```
Mentions: OeisA78590.a
theorem OeisA78590.conjecture sorry line 74 source
depends on sorry what this means
Statement uses: Iff, False, Nat, LE.le, OfNat.ofNat, Dvd.dvd, OeisA78590.a, HSub.hSub, HAdd.hAdd, HPow.hPow
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
22 instances, coercions and auxiliary constants left out.

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