260194.lean`

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

12 declarations, 1 contain sorry, 0 declared as axioms

A GCD-Driven Sequence with Universal Jumps

OEIS A260194 begins with three ones and then adds the greatest common divisor of the current term and the term two places earlier. The open question asks whether every positive integer occurs as an adjacent difference.

References:

OEIS A260194

Imports (1)

FormalConjecturesUtil

def OeisA260194.a OEIS A260194, shifted so that Lean index zero is the first OEIS term, with recurrence $a(n+3) = a(n+2) + \gcd(a(n+2),a(n))$ and initial values $a(0)=a(1)=a(2)=1$ line 39 source
Source documentation
OEIS A260194, shifted so that Lean index zero is the first OEIS term, with recurrence $a(n+3) = a(n+2) + \gcd(a(n+2),a(n))$ and initial values $a(0)=a(1)=a(2)=1$.

no axioms what this means
Statement uses: Nat
2 instances, coercions and auxiliary constants left out.
```
def a : ℕ → ℕ
  | 0 => 1
  | 1 => 1
  | 2 => 1
  | n + 3 => a (n + 2) + Nat.gcd (a (n + 2)) (a n)

@[category test, AMS 11]
```
Mentions: test, AMS
theorem OeisA260194.a_0 line 46 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_1 line 49 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_2 line 52 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_3 line 55 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_4 line 58 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_5 line 61 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_6 line 64 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_7 line 67 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_8 line 70 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.a_9 line 73 source
no axioms what this means
Statement uses: Eq, Nat, OeisA260194.a, OfNat.ofNat
Proof uses: Eq.refl
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA260194.conjecture Does every positive integer occur as a difference in this sequence? sorry line 79 source
Source documentation
Does every positive integer occur as a difference in this sequence?

depends on sorry what this means
Statement uses: Iff, True, Nat, GT.gt, OfNat.ofNat, Exists, Eq, OeisA260194.a, HAdd.hAdd
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture :
    answer(sorry) ↔ ∀ d > 0, ∃ n, a (n + 1) = a n + d := by
…
```
Mentions: OeisA260194.a