236.lean`

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L4DEL: Lean4 Domain Explanation Language

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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 236

Reference: erdosproblems.com/236

Imports (1)

FormalConjecturesUtil

def Erdos236.f $f(n)$ counts the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$ line 35 source
Source documentation
$f(n)$ counts the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: List.length, List.filter, Decidable.decide, Nat.Prime, HSub.hSub, HPow.hPow, OfNat.ofNat, List.range, HAdd.hAdd, Nat.log2
10 instances, coercions and auxiliary constants left out.
```
def f (n : ℕ) : ℕ :=
…
```
theorem Erdos236.erdos_236 Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$ sorry line 42 source
Source documentation
Let $f(n)$ count the number of solutions to $n=p+2^k$ for prime $p$ and $k\geq 0$. Show that $f(n)=o(\log n)$.

depends on sorry what this means
Statement uses: Asymptotics.IsLittleO, Nat, Real, Filter.atTop, Erdos236.f, Real.log
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
9 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_236: (fun n => (f n : ℝ)) =o[atTop] (fun n => Real.log (n : ℝ)) := by
…
```
Mentions: Erdos236.f