$$ \text{\Huge Amazing Graphs} $$

Programming and Plotting Graphs From the Numberphile Amazing Graphs Series

Table of Contents

• About the Project
• How to Use This Code
  • Installing Matplotlib
• Presentation of the Sequences
  • A002487 - Stern's Sequence
  • A005185 - Hofstadter's Q Sequence
  • A006577 - Number of Steps for N to Reach 1 in '3n+1' Problem (Bonus)
  • A063543 - Wisteria
  • A117966 - Balanced Ternary
  • A133058 - Fly straight, dammit !
  • A229037 - Forest Fire
  • A265326 - Primes
  • A279125 - Rémy Sigrist
• License

About the Project

On August 2019, the Numberphile YouTube channel posted a series of three videos in which the mathematician Neil J. A. Sloane presents amazing graphs generated by particular mathematical sequences. I wanted to reproduce these graphs myself and I present the result in this article.

Amazing Graphs trilogy :

1. Amazing Graphs - Numberphile
2. Amazing Graphs II (including Star Wars) - Numberphile
3. Amazing Graphs III - Numberphile

Neil J. A. Sloane is known for having founded the OEIS, a book and then a website on which hundreds of thousands of mathematical sequences are referenced. I strongly encourage you to visit the OEIS website.

How to Use This Code

To run this code, you will need the Matplotlib library. Matplotlib is a complete library for creating static, animated and interactive visualizations in Python.

Installing Matplotlib

You will find all the information necessary for its installation on the following page : https://matplotlib.org/users/installing.html

Presentation of the Sequences

• A002487 - Stern's Sequence

$$a_0 = 0, \quad a_1 = 1,$$

$$ \forall n \in \mathbb{N}^\star, \begin{cases} a_{2n} &= a_n \\ a_{2n+1} &= a_{n+1} + a_n \end{cases} . $$

Scatterplot of $\mathrm{A}002487(n)$

Links

OEIS page : https://oeis.org/A002487.
Amazing Graphs III - Numberphile : https://youtu.be/j0o-pMIR8uk.

• A005185 - Hofstadter's Q Sequence

$$a_1 = a_2 = 1,$$

$$\forall n > 2, a_n = a_{n - a_{n-1}} + a_{n - a_{n-2}}.$$

Scatterplot of $\mathrm{A}005185(n)$

Links

OEIS page : https://oeis.org/A005185.
Amazing Graphs III - Numberphile : https://youtu.be/j0o-pMIR8uk?t=116.

• A006577 - Number of Steps for N to Reach 1 in '3n+1' Problem (Bonus)

  ❕ This graph is not presented in Numberphile's trilogy but I still want to share it with you

  Scatterplot of $\mathrm{A}006577(n)$

  

  Links

  OEIS page : https://oeis.org/A006577.
  UNCRACKABLE? The Collatz Conjecture - Numberphile : https://youtu.be/5mFpVDpKX70.

• A063543 - Wisteria

$$ a_n = n - \text{product of nonzero digits of } n.$$

Scatterplot of $\mathrm{A}063543(n)$

Links

OEIS page : https://oeis.org/A063543.
Amazing Graphs II (including Star Wars) - Numberphile : https://youtu.be/o8c4uYnnNnc?t=110.

• A117966 - Balanced Ternary

  Scatterplot of $\mathrm{A}117966(n)$

  

  Links

  OEIS page : https://oeis.org/A117966.
  Amazing Graphs II (including Star Wars) - Numberphile : https://youtu.be/o8c4uYnnNnc?.

• A133058 - Fly straight, dammit !

$$a_0 = a_1 = 1,$$

$$ \forall n > 1, \begin{cases} a_n &= a_{n-1} + n + 1 &\text{if $a_{n-1}$ and $n$ are coprime} \\ a_n &= \displaystyle \frac{a_{n-1}}{\mathrm{gcd}(a_{n-1}, n)} &\text{otherwise} \end{cases} . $$

Scatterplot of $\mathrm{A}133058(n)$

Links

OEIS page : https://oeis.org/A133058.
Amazing Graphs - Numberphile : https://youtu.be/pAMgUB51XZA?t=96.

• A229037 - Forest Fire

  Scatterplot of $\mathrm{A}229037(n)$

  

  Links

  OEIS page : https://oeis.org/A229037.
  Amazing Graphs II (including Star Wars) - Numberphile : https://youtu.be/o8c4uYnnNnc?t=217.

• A265326 - Primes

$$ n\text{-th prime minus its binary reversal}.$$

Scatterplot of $\mathrm{A}265326(n)$

Links

OEIS page : https://oeis.org/A265326.
Amazing Graphs - Numberphile : https://youtu.be/pAMgUB51XZA?t=469.

• A279125 - Rémy Sigrist

  Scatterplot of $\mathrm{A}279125(n)$

  

  Links

  OEIS page : https://oeis.org/A279125.
  Amazing Graphs III - Numberphile : https://youtu.be/j0o-pMIR8uk?t=369.

License

Distributed under the MIT License. See LICENSE for more information.