80101.lean`

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L4DEL: Lean4 Domain Explanation Language

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

6 declarations, 1 contain sorry, 0 declared as axioms

Number of prime powers strictly between $n$-th prime and $(n+1)$-th prime

The sequence $a(n)$ is the number of prime powers $k$ strictly between the $n$-th prime $p_n$ and the $(n+1)$-th prime $p_{n+1}$: $p_n < k < p_{n+1}$.

References:

A080101

Imports (1)

FormalConjecturesUtil

def OeisA80101.a Number of prime powers strictly between the $n$-th prime and the $(n+1)$-th prime line 36 source
Source documentation
Number of prime powers strictly between the $n$-th prime and the $(n+1)$-th prime.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: ite, Eq, OfNat.ofNat, Nat.nth, Nat.Prime, HSub.hSub, Finset.card, Finset.filter, IsPrimePow, Finset.Ioo
8 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
theorem OeisA80101.a_1 Value of the sequence a at 1 line 45 source
Source documentation
Value of the sequence a at 1.

extra axioms: _private.0.OeisA80101.a_1._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA80101.a, OfNat.ofNat
Proof uses: id, Eq.mpr, Finset.card, Finset.filter, IsPrimePow, Finset.Ioo, Nat.nth, Nat.Prime, congrArg, Nat.nth_prime_zero_eq_two, Nat.nth_prime_one_eq_three, of_decide_eq_true
8 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 0 := by
…
```
Mentions: OeisA80101.a
theorem OeisA80101.a_2 Value of the sequence a at 2 line 52 source
Source documentation
Value of the sequence a at 2.

extra axioms: _private.0.OeisA80101.a_2._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA80101.a, OfNat.ofNat
Proof uses: id, Eq.mpr, Finset.card, Finset.filter, IsPrimePow, Finset.Ioo, Nat.nth, Nat.Prime, congrArg, Nat.nth_prime_one_eq_three, Nat.nth_prime_two_eq_five, of_decide_eq_true
8 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
theorem a_2 : a 2 = 1 := by
…
```
Mentions: OeisA80101.a
theorem OeisA80101.a_3 Value of the sequence a at 3 line 59 source
Source documentation
Value of the sequence a at 3.

extra axioms: _private.0.OeisA80101.a_3._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA80101.a, OfNat.ofNat
Proof uses: id, Eq.mpr, Finset.card, Finset.filter, IsPrimePow, Finset.Ioo, Nat.nth, Nat.Prime, congrArg, Nat.nth_prime_two_eq_five, Nat.nth_prime_three_eq_seven, of_decide_eq_true
8 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : a 3 = 0 := by
…
```
Mentions: OeisA80101.a
theorem OeisA80101.a_4 Value of the sequence a at 4 line 66 source
Source documentation
Value of the sequence a at 4.

extra axioms: _private.0.OeisA80101.a_4._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA80101.a, OfNat.ofNat
Proof uses: id, Eq.mpr, Finset.card, Finset.filter, IsPrimePow, Finset.Ioo, Nat.nth, Nat.Prime, congrArg, Nat.nth_prime_three_eq_seven, Nat.nth_prime_four_eq_eleven, of_decide_eq_true
8 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
theorem a_4 : a 4 = 2 := by
…
```
Mentions: OeisA80101.a
theorem OeisA80101.conjecture It is conjectured that $a(n) \le 2$ for all $n$ sorry line 74 source
Source documentation
It is conjectured that $a(n) \le 2$ for all $n$.

depends on sorry what this means
Statement uses: Nat, LE.le, OeisA80101.a, OfNat.ofNat
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) : a n ≤ 2 := by
…
```
Mentions: OeisA80101.a