102847.lean`

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L4DEL: Lean4 Domain Explanation Language

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

10 declarations, 1 contain sorry, 0 declared as axioms

$a(0) = 1$, $a(n) = a(n-1)a(n-1) + 2$

References:

A102847

Imports (1)

FormalConjecturesUtil

def OeisA102847.a The primary defining sequence a line 33 source
Source documentation
The primary defining sequence a. $a(0)=1$, $a(n) = a(n-1)^2 + 2$.

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

/-- Term theorems verifying the first few values of the sequence against the official OEIS b-file -/
@[category test, AMS 11]
```
Mentions: test, AMS
theorem OeisA102847.a_0 Term theorems verifying the first few values of the sequence against the official OEIS b-file line 39 source
Source documentation
Term theorems verifying the first few values of the sequence against the official OEIS b-file

standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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_0 : a 0 = 1 := by rfl
…
```
Mentions: OeisA102847.a
theorem OeisA102847.a_1 line 42 source
standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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 OeisA102847.a_2 line 45 source
standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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 OeisA102847.a_3 line 48 source
standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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 OeisA102847.a_4 line 51 source
standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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 OeisA102847.a_5 line 54 source
standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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 OeisA102847.a_6 line 57 source
standard axioms: propext what this means
Statement uses: Eq, Nat, OeisA102847.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 OeisA102847.not_prime_a_5 line 60 source
standard axioms: propext what this means
Statement uses: Not, Nat.Prime, OeisA102847.a, OfNat.ofNat, Nat
Proof uses: Eq, HMul.hMul, Eq.mpr, id, congrArg, OeisA102847.a_5, Eq.refl, Nat.not_prime_mul, of_decide_eq_true, Ne, Bool, Decidable.decide, Bool.true
6 instances, coercions and auxiliary constants left out.

Tactic trace: 6 steps
Open to load the checked before-and-after goal states.
theorem OeisA102847.conjecture Prime for $a(1) = 3$, $a(2) = 11$, $a(4) = 15131$; semiprime for $a(3) = 123 = 3 * 41$, $a(5) = 228947163 = 3 * 76315721$ sorry line 73 source
Source documentation
Prime for $a(1) = 3$, $a(2) = 11$, $a(4) = 15131$; semiprime for $a(3) = 123 = 3 * 41$, $a(5) = 228947163 = 3 * 76315721$. $a(6)$, added by Jonathan Vos Post, has 4 prime factors. $a(7) = 41 * 811^2 * 106693969 * 317171188688357726699 * 8272236925540996054440172449761$. When is the next prime in the sequence?

depends on sorry what this means
Statement uses: Eq, Nat, sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, InfSet.sInf, Set.ofPred, And, LT.lt, Nat.Prime, OeisA102847.a
6 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) = sInf {n : ℕ | 4 < n ∧ (a n).Prime} := by
…
```
Mentions: OeisA102847.a