108129.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Riesel Problem

Riesel problem: let $k=2n-1$; then $a(n)$ is the smallest $m \ge 1$ such that $k \cdot 2^m-1$ is prime, or $-1$ if no such prime exists.

References:

A108129

Imports (1)

FormalConjecturesUtil

def OeisA108129.a The primary defining sequence a line 41 source
Source documentation
The primary defining sequence a. Riesel problem: let $k=2n-1$; then $a(n)$ is the smallest $m \ge 1$ such that $k \cdot 2^m-1$ is prime, or $-1$ if no such prime exists.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Int
Proof uses: ite, Eq, OfNat.ofNat, dite, Exists, And, Ne, Nat.Prime, HSub.hSub, HMul.hMul, HPow.hPow, Classical.propDecidable, Nat.find, Not, Neg.neg
17 instances, coercions and auxiliary constants left out.
```
noncomputable def a (n : ℕ) : ℤ :=
…
```
lemma OeisA108129.a_of_isLeast line 50 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, IsLeast, Set.ofPred, And, Ne, OfNat.ofNat, Nat.Prime, HSub.hSub, HMul.hMul, HPow.hPow, Eq, Int, OeisA108129.a
Proof uses: False, False.elim, Eq.mp, Membership.mem, Set, Eq.trans, EmptyCollection.emptyCollection, congrFun', congrArg, funext, Not, MulZeroClass.mul_zero, zero_tsub, MulZeroClass.zero_mul, and_false, And.left, lowerBounds, Eq.symm, Eq.mpr, ite and 12 more
46 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
theorem OeisA108129.a_1 line 57 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Int, OeisA108129.a, OfNat.ofNat, Nat
Proof uses: OeisA108129.a_of_isLeast, of_decide_eq_true, IsLeast, Set.ofPred, And, Ne, Nat.Prime, HSub.hSub, HMul.hMul, HPow.hPow, id, Bool, Decidable.decide, Bool.true, Eq.refl
17 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA108129.a_2 line 60 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Int, OeisA108129.a, OfNat.ofNat, Nat
Proof uses: OeisA108129.a_of_isLeast, of_decide_eq_true, IsLeast, Set.ofPred, And, Ne, Nat.Prime, HSub.hSub, HMul.hMul, HPow.hPow, id, Bool, Decidable.decide, Bool.true, Eq.refl
17 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA108129.a_3 line 63 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Int, OeisA108129.a, OfNat.ofNat, Nat
Proof uses: OeisA108129.a_of_isLeast, of_decide_eq_true, IsLeast, Set.ofPred, And, Ne, Nat.Prime, HSub.hSub, HMul.hMul, HPow.hPow, id, Bool, Decidable.decide, Bool.true, Eq.refl
17 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA108129.a_4 line 66 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Int, OeisA108129.a, OfNat.ofNat, Nat
Proof uses: OeisA108129.a_of_isLeast, of_decide_eq_true, IsLeast, Set.ofPred, And, Ne, Nat.Prime, HSub.hSub, HMul.hMul, HPow.hPow, id, Bool, Decidable.decide, Bool.true, Eq.refl
17 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA108129.conjecture It is conjectured that the integer $k = 509203$ is the smallest Riesel number, that is, the first $n$ such that $a(n) = -1$ is $254602$ sorry line 73 source
Source documentation
It is conjectured that the integer $k = 509203$ is the smallest Riesel number, that is, the first $n$ such that $a(n) = -1$ is $254602$.

depends on sorry what this means
Statement uses: And, Eq, Int, OeisA108129.a, OfNat.ofNat, Nat, Neg.neg, LE.le, LT.lt, Ne
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture :
    a 254602 = -1 ∧ (∀ n : ℕ, 1 ≤ n ∧ n < 254602 → a n ≠ -1) := by
…
```
Mentions: OeisA108129.a