113257.lean`

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

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

8 declarations, 2 contain sorry, 0 declared as axioms

Ascending descending base exponent transform of squares

a n is $\sum_{i=1}^n (i^2)^((n-i+1)^2)$.

References:

A113257

Imports (1)

FormalConjecturesUtil

def OeisA113257.a a n is the ascending descending base exponent transform of squares line 34 source
Source documentation
a n is the ascending descending base exponent transform of squares

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.sum, Finset.Icc, OfNat.ofNat, HPow.hPow, HAdd.hAdd, HSub.hSub
12 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA113257.a_1 line 38 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA113257.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 OeisA113257.a_2 line 41 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA113257.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 OeisA113257.a_3 line 44 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA113257.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 OeisA113257.a_4 line 47 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA113257.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 OeisA113257.a_5 line 50 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA113257.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 OeisA113257.conjecture1 The smallest prime in this sequence is $a(2) = 5$ sorry line 56 source
Source documentation
The smallest prime in this sequence is $a(2) = 5$. What is the next prime?

depends on sorry what this means
Statement uses: Eq, Nat, sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, OeisA113257.a, InfSet.sInf, Set.ofPred, And, LT.lt, Nat.Prime
6 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture1 :
    answer(sorry) = a (sInf {n : ℕ | 2 < n ∧ (a n).Prime}) := by
…
```
Mentions: OeisA113257.a
theorem OeisA113257.conjecture2 What is the first square value after 1? sorry line 64 source
Source documentation
What is the first square value after 1?

depends on sorry what this means
Statement uses: Eq, Nat, sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, OeisA113257.a, InfSet.sInf, Set.ofPred, And, LT.lt, IsSquare
8 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture2 :
    answer(sorry) = a (sInf {n : ℕ | 1 < n ∧ IsSquare (a n)}) := by
…
```
Mentions: OeisA113257.a