105801.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Fibonacci-Collatz sequence

Fibonacci-Collatz sequence: $a(1)=1, a(2)=2$; for $n > 2$, let $\mathrm{fib} = a(n-1) + a(n-2)$; if $\mathrm{fib}$ is odd then $a(n) = 3 \cdot \mathrm{fib} + 1$ else $a(n) = \mathrm{fib}/2$.

References:

A105801

Imports (1)

FormalConjecturesUtil

def OeisA105801.a The primary defining sequence a line 38 source
Source documentation
The primary defining sequence a. $a(n)$ is the Fibonacci-Collatz sequence: $a(1)=1, a(2)=2$; for $n > 2$, let $\mathrm{fib} = a(n-1) + a(n-2)$; if $\mathrm{fib}$ is odd then $a(n) = 3 \cdot \mathrm{fib} + 1$ else $a(n) = \mathrm{fib}/2$.

no axioms what this means
Statement uses: Nat
2 instances, coercions and auxiliary constants left out.
```
def a : ℕ → ℕ
  | 0 => 0 -- The sequence is 1-indexed, a(0) is a conventional filler.
  | 1 => 1
  | 2 => 2
  | n + 3 =>
    let fib := a (n + 2) + a (n + 1)
…
```
theorem OeisA105801.a_1 Term theorems verifying the first few values of the sequence against the official OEIS b-file line 48 source
Source documentation
Term theorems verifying the first few values of the sequence against the official OEIS b-file

no axioms what this means
Statement uses: Eq, Nat, OeisA105801.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 = 1 := by decide
…
```
Mentions: OeisA105801.a
theorem OeisA105801.a_2 line 51 source
no axioms what this means
Statement uses: Eq, Nat, OeisA105801.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 OeisA105801.a_3 line 54 source
no axioms what this means
Statement uses: Eq, Nat, OeisA105801.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 OeisA105801.a_4 line 57 source
no axioms what this means
Statement uses: Eq, Nat, OeisA105801.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 OeisA105801.a_5 line 60 source
no axioms what this means
Statement uses: Eq, Nat, OeisA105801.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 OeisA105801.conjecture sorry line 69 source
depends on sorry what this means
Statement uses: Nat, LT.lt, OfNat.ofNat, Exists, Nat.ModEq, HPow.hPow, OeisA105801.a, HAdd.hAdd
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
16 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.