93818.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

$\gcd(\mathrm{numerator}(H_n), n!)$

$a(n) = \gcd(\mathrm{A001008}(n), n!)$, where $\mathrm{A001008}(n)$ is the numerator of the $n$-th harmonic number $H_n = \sum_{i=1}^n \frac{1}{i}$.

References:

A093818

Imports (1)

FormalConjecturesUtil

def OeisA93818.a $a(n) = \gcd(\mathrm{numerator}(H_n), n!)$, where $H_n$ is the $n$-th harmonic number line 35 source
Source documentation
$a(n) = \gcd(\mathrm{numerator}(H_n), n!)$, where $H_n$ is the $n$-th harmonic number.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Nat.gcd, Int.natAbs, Rat.num, harmonic, Nat.factorial
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA93818.a_0 Value of the sequence a at 0 line 40 source
Source documentation
Value of the sequence a at 0.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA93818.a, OfNat.ofNat
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 decide +kernel
…
```
Mentions: OeisA93818.a
theorem OeisA93818.a_1 Value of the sequence a at 1 line 44 source
Source documentation
Value of the sequence a at 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA93818.a, OfNat.ofNat
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 decide +kernel
…
```
Mentions: OeisA93818.a
theorem OeisA93818.a_2 Value of the sequence a at 2 line 48 source
Source documentation
Value of the sequence a at 2.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA93818.a, OfNat.ofNat
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 decide +kernel
…
```
Mentions: OeisA93818.a
theorem OeisA93818.a_3 Value of the sequence a at 3 line 52 source
Source documentation
Value of the sequence a at 3.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA93818.a, OfNat.ofNat
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 = 1 := by decide +kernel
…
```
Mentions: OeisA93818.a
theorem OeisA93818.a_4 Value of the sequence a at 4 line 56 source
Source documentation
Value of the sequence a at 4.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA93818.a, OfNat.ofNat
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 = 1 := by decide +kernel
…
```
Mentions: OeisA93818.a
theorem OeisA93818.conjecture Conjecture: Every odd prime occurs as a term in the sequence sorry line 61 source
Source documentation
Conjecture: Every odd prime occurs as a term in the sequence.

depends on sorry what this means
Statement uses: Nat, Nat.Prime, Ne, OfNat.ofNat, Exists, And, GT.gt, Eq, OeisA93818.a
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 (p : ℕ) (hp : p.Prime) (hp_odd : p ≠ 2) : ∃ n > 0, a n = p := by
…
```
Mentions: OeisA93818.a