103151.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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

7 declarations, 1 contain sorry, 0 declared as axioms

Number of decompositions of $2n+1$ into $2p+q$, where $p$ and $q$ are both odd primes

References:

A103151

Imports (1)

FormalConjecturesUtil

def OeisA103151.a The primary defining sequence a line 35 source
Source documentation
The primary defining sequence a. a n is the number of decompositions of 2n+1 into 2p+q, where p and q are both odd primes.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.card, Finset.filter, And, Nat.Prime, Ne, OfNat.ofNat, LT.lt, HMul.hMul, HAdd.hAdd, HSub.hSub, Eq, Finset.range
13 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA103151.a_1 Term theorems verifying the first few values of the sequence against the official OEIS b-file line 50 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, OeisA103151.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 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 = 0 := by decide
…
```
Mentions: OeisA103151.a
theorem OeisA103151.a_2 line 53 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA103151.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA103151.a_3 line 56 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA103151.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA103151.a_4 line 59 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA103151.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA103151.a_5 line 62 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA103151.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA103151.conjecture Conjecture: all items for $n \ge 4$ are greater than or equal to $1$ sorry line 69 source
Source documentation
Conjecture: all items for $n \ge 4$ are greater than or equal to $1$. This is a stronger conjecture than the Goldbach conjecture.

depends on sorry what this means
Statement uses: Nat, GE.ge, OfNat.ofNat, OeisA103151.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 (n : ℕ) (hn : n ≥ 4) : a n ≥ 1 := by
…
```
Mentions: OeisA103151.a