110835.lean`

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L4DEL: Lean4 Domain Explanation Language

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

5 declarations, 1 contain sorry, 0 declared as axioms

Smallest $m > 0$ such that there are no primes between $nm$ and $n(m+1)$ inclusive.

Sierpinski's conjecture (1958) is precisely that a(n) >= n for all n.

References:

A110835

Imports (1)

FormalConjecturesUtil

def OeisA110835.a The primary defining sequence a line 40 source
Source documentation
The primary defining sequence a. $a(n)$ is the smallest $m > 0$ such that there are no primes between $n \cdot m$ and $n \cdot (m+1)$ inclusive.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Nat.Prime, Not, And, LE.le, HMul.hMul, HAdd.hAdd, OfNat.ofNat, Set, Set.ofPred, GT.gt, InfSet.sInf
8 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℕ :=
…
```
theorem OeisA110835.a_1 Term theorems verifying the first few values of the sequence against the official OEIS b-file line 48 source
Source documentation
Term theorems verifying the first few values of the sequence against the official OEIS b-file

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA110835.a, OfNat.ofNat
Proof uses: id, IsLeast, Set.ofPred, And, GT.gt, Nat.Prime, Not, LE.le, HMul.hMul, HAdd.hAdd, And.intro, Membership.mem, Set, lowerBounds, Eq.mpr, congrFun', congrArg, funext, forall_congr, implies_congr and 25 more
35 instances, coercions and auxiliary constants left out.

Tactic trace: 52 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 8 := by
…
```
Mentions: OeisA110835.a
theorem OeisA110835.a_2 line 70 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA110835.a, OfNat.ofNat
Proof uses: id, IsLeast, Set.ofPred, And, GT.gt, Nat.Prime, Not, LE.le, HMul.hMul, HAdd.hAdd, And.intro, Membership.mem, Set, lowerBounds, of_decide_eq_true, Bool, Decidable.decide, Bool.true, Eq.refl, False and 18 more
37 instances, coercions and auxiliary constants left out.

Tactic trace: 31 steps
Open to load the checked before-and-after goal states.
theorem OeisA110835.a_3 line 87 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA110835.a, OfNat.ofNat
Proof uses: id, IsLeast, Set.ofPred, And, GT.gt, Nat.Prime, Not, LE.le, HMul.hMul, HAdd.hAdd, And.intro, Membership.mem, Set, lowerBounds, of_decide_eq_true, Bool, Decidable.decide, Bool.true, Eq.refl, False and 18 more
37 instances, coercions and auxiliary constants left out.

Tactic trace: 51 steps
Open to load the checked before-and-after goal states.
theorem OeisA110835.conjecture Sierpinski's conjecture (1958) is precisely that $a(n) >= n$ for all $n$ sorry line 111 source
Source documentation
Sierpinski's conjecture (1958) is precisely that $a(n) >= n$ for all $n$.

depends on sorry what this means
Statement uses: Nat, GT.gt, OfNat.ofNat, GE.ge, OeisA110835.a
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture : ∀ n > 0, a n ≥ n := by
…
```
Mentions: OeisA110835.a