101779.lean`

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L4DEL: Lean4 Domain Explanation Language

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

8 declarations, 1 contain sorry, 0 declared as axioms

Conjectures associated with A101779

$a(n)$ is the least $k$ such that all of $k, 2k+1, 3k+2, ..., nk+n-1$ are primes, or $0$ if no such $k$ is found. It is conjectured $k$ always exists.

References:

A101779

Imports (1)

FormalConjecturesUtil

def OeisA101779.Ak A101779: Ak n k is true if for all $i$ from $1$ to $n$, $i \cdot k + (i - 1)$ is prime line 41 source
Source documentation
A101779: Ak n k is true if for all $i$ from $1$ to $n$, $i \cdot k + (i - 1)$ is prime.

standard axioms: propext what this means
Statement uses: Nat
Proof uses: LE.le, OfNat.ofNat, Nat.Prime, HAdd.hAdd, HMul.hMul, HSub.hSub
8 instances, coercions and auxiliary constants left out.
```
def Ak (n k : ℕ) : Prop :=
…
```
instance OeisA101779.(instance at line 44) line 44 source
def OeisA101779.a The primary defining sequence a line 52 source
Source documentation
The primary defining sequence a. $a(n)$ is the least $k$ such that all of $k, 2k+1, 3k+2, \ldots, nk+n-1$ are primes, or $0$ if no such $k$ is found.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: InfSet.sInf, Set.ofPred, OeisA101779.Ak
1 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
theorem OeisA101779.a_1 line 56 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA101779.a, OfNat.ofNat
Proof uses: IsLeast.csInf_eq, Set.ofPred, OeisA101779.Ak, of_decide_eq_true, IsLeast, id, Bool, Decidable.decide, Bool.true, Eq.refl
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA101779.a_2 line 59 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA101779.a, OfNat.ofNat
Proof uses: IsLeast.csInf_eq, Set.ofPred, OeisA101779.Ak, of_decide_eq_true, IsLeast, id, Bool, Decidable.decide, Bool.true, Eq.refl
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA101779.a_3 line 62 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA101779.a, OfNat.ofNat
Proof uses: IsLeast.csInf_eq, Set.ofPred, OeisA101779.Ak, of_decide_eq_true, IsLeast, id, Bool, Decidable.decide, Bool.true, Eq.refl
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA101779.a_4 line 65 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA101779.a, OfNat.ofNat
Proof uses: IsLeast.csInf_eq, Set.ofPred, OeisA101779.Ak, of_decide_eq_true, IsLeast, id, Bool, Decidable.decide, Bool.true, Eq.refl
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA101779.conjecture It is conjectured k always exists sorry line 71 source
Source documentation
It is conjectured k always exists.

depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Exists, OeisA101779.Ak
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 : ∀ (n : ℕ), 1 ≤ n → ∃ k : ℕ, Ak n k := by
…
```
Mentions: OeisA101779.Ak