Gilbreath.lean`

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

2 declarations, 1 contain sorry, 0 declared as axioms

Gilbreath's conjecture

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100OpenSet1.lean

def Gilbreath.d Gilbreath's nth difference, $d^n$ Let $d^0(n) = p_n$ and $d^k(n) = |d^{k-1}(n+1) - d^{k-1}(n)|$ line 34 source
Source documentation
Gilbreath's nth difference, $d^n$ Let $d^0(n) = p_n$ and $d^k(n) = |d^{k-1}(n+1) - d^{k-1}(n)|$

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
2 instances, coercions and auxiliary constants left out.
```
noncomputable def d : ℕ → (ℕ → ℕ)
  | 0 => fun n ↦ n.nth Nat.Prime
  | k + 1 => fun n ↦ Int.natAbs (d k (n + 1) - d k n)

open Gilbreath

/--
**Gilbreath's conjecture**
Gilbreath's conjecture states that every term in the sequence $d^k_0$ for $k > 0$ is equal to 1.
-/
@[category research open, AMS 11]
```
Mentions: AMS
theorem Gilbreath.gilbreath_conjecture Gilbreath's conjecture Gilbreath's conjecture states that every term in the sequence $d^k_0$ for $k > 0$ is equal to 1 sorry line 45 source
Source documentation
Gilbreath's conjecture Gilbreath's conjecture states that every term in the sequence $d^k_0$ for $k > 0$ is equal to 1.

depends on sorry what this means
Statement uses: PNat, Eq, Nat, Gilbreath.d, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem gilbreath_conjecture (k : ℕ+) : d k 0 = 1 := by
…
```
Mentions: Gilbreath.d