84046.lean`

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

6 declarations, 1 contain sorry, 0 declared as axioms

Smallest prime $p$ such that $p + n$ is an $n$-th power

Smallest prime $p$ such that $p + n$ is an $n$-th power, or $0$ if no such number exists. That is, the smallest prime of the form $k^n - n$.

References:

A084046

Imports (1)

FormalConjecturesUtil

def OeisA84046.a Smallest prime $p$ such that $p + n$ is an $n$-th power, or $0$ if no such prime exists line 34 source
Source documentation
Smallest prime $p$ such that $p + n$ is an $n$-th power, or $0$ if no such prime exists.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: InfSet.sInf, Set.ofPred, And, Nat.Prime, Exists, Eq, HPow.hPow, HAdd.hAdd
7 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
theorem OeisA84046.a_0 Value of the sequence a at 0 line 39 source
Source documentation
Value of the sequence a at 0.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA84046.a, OfNat.ofNat
Proof uses: id, Set, Set.ofPred, And, Nat.Prime, Exists, HPow.hPow, HAdd.hAdd, EmptyCollection.emptyCollection, Set.ext, Eq.mpr, Iff, Membership.mem, Not, Eq.trans, False, congrArg, iff_false, Nat.not_prime_one, Eq.mp and 5 more
25 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
theorem a_0 : a 0 = 0 := by
…
```
Mentions: OeisA84046.a
theorem OeisA84046.a_1 Value of the sequence a at 1 line 52 source
Source documentation
Value of the sequence a at 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA84046.a, OfNat.ofNat
Proof uses: IsLeast, Set.ofPred, And, Nat.Prime, Exists, HPow.hPow, HAdd.hAdd, And.intro, Membership.mem, Set, lowerBounds, id, Nat.prime_two, Exists.intro, Mathlib.Meta.NormNum.isNat_eq_true, Mathlib.Meta.NormNum.isNat_pow, Eq.refl, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.natPow_one, Mathlib.Meta.NormNum.isNat_add and 3 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 11 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 2 := by
…
```
Mentions: OeisA84046.a
theorem OeisA84046.a_2 Value of the sequence a at 2 line 64 source
Source documentation
Value of the sequence a at 2.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA84046.a, OfNat.ofNat
Proof uses: IsLeast, Set.ofPred, And, Nat.Prime, Exists, HPow.hPow, HAdd.hAdd, And.intro, Membership.mem, Set, lowerBounds, id, Nat.prime_two, Exists.intro, Mathlib.Meta.NormNum.isNat_eq_true, Mathlib.Meta.NormNum.isNat_pow, Eq.refl, Mathlib.Meta.NormNum.isNat_ofNat, Mathlib.Meta.NormNum.IsNatPowT.run, Mathlib.Meta.NormNum.IsNatPowT.bit0 and 4 more
20 instances, coercions and auxiliary constants left out.

Tactic trace: 11 steps
Open to load the checked before-and-after goal states.
```
theorem a_2 : a 2 = 2 := by
…
```
Mentions: OeisA84046.a
theorem OeisA84046.a_3 Value of the sequence a at 3 line 76 source
Source documentation
Value of the sequence a at 3.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA84046.a, OfNat.ofNat
Proof uses: IsLeast, Set.ofPred, And, Nat.Prime, Exists, HPow.hPow, HAdd.hAdd, And.intro, Membership.mem, Set, lowerBounds, id, Mathlib.Meta.NormNum.isNat_prime_2, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.true, Mathlib.Meta.NormNum.isNat_minFac_4, Mathlib.Meta.NormNum.IsNat.raw_refl, Mathlib.Meta.NormNum.minFacHelper_0 and 30 more
43 instances, coercions and auxiliary constants left out.

Tactic trace: 45 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : a 3 = 5 := by
…
```
Mentions: OeisA84046.a
theorem OeisA84046.conjecture sorry line 111 source
depends on sorry what this means
Statement uses: Not, Nat, Eq, OeisA84046.a, OfNat.ofNat, Exists, HPow.hPow, HMul.hMul
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
14 instances, coercions and auxiliary constants left out.

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