96535.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Recurrence $a(n) = (a(n-1) + a(n-2)) \pmod n$

$a(0) = a(1) = 1$; $a(n) = (a(n-1) + a(n-2)) \pmod n$.

References:

A096535

Imports (1)

FormalConjecturesUtil

def OeisA96535.a Recurrence $a(n) = (a(n-1) + a(n-2)) \pmod n$ line 33 source
Source documentation
Recurrence $a(n) = (a(n-1) + a(n-2)) \pmod n$.

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

/-- Value of the sequence `a` at 0. -/
@[category test, AMS 11]
```
Mentions: test, AMS
theorem OeisA96535.a_0 Value of the sequence a at 0 line 40 source
Source documentation
Value of the sequence a at 0.

no axioms what this means
Statement uses: Eq, Nat, OeisA96535.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 a_0 : a 0 = 1 := by rfl
…
```
Mentions: OeisA96535.a
theorem OeisA96535.a_1 Value of the sequence a at 1 line 44 source
Source documentation
Value of the sequence a at 1.

no axioms what this means
Statement uses: Eq, Nat, OeisA96535.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 a_1 : a 1 = 1 := by rfl
…
```
Mentions: OeisA96535.a
theorem OeisA96535.a_2 Value of the sequence a at 2 line 48 source
Source documentation
Value of the sequence a at 2.

no axioms what this means
Statement uses: Eq, Nat, OeisA96535.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 a_2 : a 2 = 0 := by rfl
…
```
Mentions: OeisA96535.a
theorem OeisA96535.a_3 Value of the sequence a at 3 line 52 source
Source documentation
Value of the sequence a at 3.

no axioms what this means
Statement uses: Eq, Nat, OeisA96535.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 a_3 : a 3 = 1 := by rfl
…
```
Mentions: OeisA96535.a
theorem OeisA96535.a_4 Value of the sequence a at 4 line 56 source
Source documentation
Value of the sequence a at 4.

no axioms what this means
Statement uses: Eq, Nat, OeisA96535.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 a_4 : a 4 = 1 := by rfl
…
```
Mentions: OeisA96535.a
theorem OeisA96535.conjecture All numbers appear infinitely often, i.e., for every number sorry line 64 source
Source documentation
All numbers appear infinitely often, i.e., for every number $k \ge 0$ and every frequency $f > 0$ there is an index $i$ such that $a(i) = k$ is the $f$-th occurrence of $k$ in the sequence.
- Klaus Brockhaus, Aug 29 2006
depends on sorry what this means
Statement uses: Nat, Exists, And, GT.gt, Eq, OeisA96535.a
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture (k : ℕ) (N : ℕ) : ∃ i : ℕ, i > N ∧ a i = k := by
…
```
Mentions: OeisA96535.a