76141.lean`

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

9 declarations, 1 contain sorry, 0 declared as axioms

Number of times $n$ occurs as a binary sub-pattern of $n^2$

The sequence $a(n)$ is the number of times the binary expansion of $n$ appears as a contiguous sublist (infix) in the binary expansion of $n^2$.

References:

A076141

Imports (1)

FormalConjecturesUtil

def OeisA76141.binaryPattern The binary representation of a natural number $n$, most significant bit first line 36 source
Source documentation
The binary representation of a natural number $n$, most significant bit first. For $n = 0$, this is $[0]$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, List
Proof uses: ite, Eq, OfNat.ofNat, List.cons, List.nil, List.reverse, Nat.digits
2 instances, coercions and auxiliary constants left out.
```
def binaryPattern (n : ℕ) : List ℕ :=
…
```
def OeisA76141.a Number of times the binary pattern of $n$ occurs as an infix of the binary pattern of $n^2$ line 40 source
Source documentation
Number of times the binary pattern of $n$ occurs as an infix of the binary pattern of $n^2$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: List, OeisA76141.binaryPattern, HPow.hPow, OfNat.ofNat, List.countP, List.isPrefixOf, List.tails
7 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA76141.a_0 Value of the sequence a at 0 line 47 source
Source documentation
Value of the sequence a at 0.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA76141.a, OfNat.ofNat
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
…
```
Mentions: OeisA76141.a
theorem OeisA76141.a_1 Value of the sequence a at 1 line 52 source
Source documentation
Value of the sequence a at 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA76141.a, OfNat.ofNat
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
…
```
Mentions: OeisA76141.a
theorem OeisA76141.a_2 Value of the sequence a at 2 line 57 source
Source documentation
Value of the sequence a at 2.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA76141.a, OfNat.ofNat
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 = 1 := by
…
```
Mentions: OeisA76141.a
theorem OeisA76141.a_3 Value of the sequence a at 3 line 62 source
Source documentation
Value of the sequence a at 3.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA76141.a, OfNat.ofNat
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 = 0 := by
…
```
Mentions: OeisA76141.a
theorem OeisA76141.a_4 Value of the sequence a at 4 line 67 source
Source documentation
Value of the sequence a at 4.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA76141.a, OfNat.ofNat
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
…
```
Mentions: OeisA76141.a
theorem OeisA76141.a_5 Value of the sequence a at 5 line 72 source
Source documentation
Value of the sequence a at 5.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA76141.a, OfNat.ofNat
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_5 : a 5 = 0 := by
…
```
Mentions: OeisA76141.a
theorem OeisA76141.conjecture sorry line 80 source
depends on sorry what this means
Statement uses: Nat, LE.le, OeisA76141.a, 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.