Introduction

Python script to generate Ramanujan numbers (numbers that can be expressed as the sum of two different cubes in two different ways)

For example, 1729 = 10^3 + 9^3 = 12^3 + 1^3

where ^ denotes exponentiation.

Installation

Install R

https://www.r-project.org/

R Studio

https://www.rstudio.com/products/rstudio/download/preview/

and Python

https://www.python.org/downloads/

In R run the following commands

r install.packages('sqldf') install.packages('ggplot2')

or

r install.packages('devtools') library(devtools) devtools::install_github('neelsoumya/ramanujan_number_generator')

Clone or download the repository

r git clone https://github.com/neelsoumya/ramanujan_number_generator

Usage

python python ramanujan_test_v1.py

```r

R --no-save < analysis.R

```

Files

• ramanujan_test_v1.py

  • Usage

    nohup python3 ramanujantestv1.py

• ramanujan_numbers_list.txt

  • a list of some Ramanujan numbers in the format (2, 16, 9, 15, 4104) where 2^3 + 16^3 = 9^3 + 15^3 = 4104

• ramanujan_numbers_list2000.txt

  • a list of Ramanujan numbers upto a,b,c,d <= 2000 where a^2 + b^2 = c^2 + d^2

• ramanujan_numbers_list2001to4000.txt

  • a list of Ramanujan numbers from a,b,c,d > 2000 upto a,b,c,d <= 4000 where a^2 + b^2 = c^2 + d^2

• combined_numbers.txt

  • combined list of numbers cat ramanujan*.txt > combined_numbers.txt (, ), and done removed

• hist_ramanujan_numbers.jpg

  • histogram of Ramanujan numbers

• hist_ramanujan_numbers_log10.eps

  * histogram of Ramanujan numbers
  
  * generated using analysis.R
  

• hist_ramanujan_numbers.eps

  • histogram of Ramanujan numbers

• ALL.txt

  • All Ramanujan numbers

Contact

Soumya Banerjee

https://sites.google.com/site/neelsoumya

sb2333@cam.ac.uk

Other ideas and resources

https://stackoverflow.com/questions/69669784/ramanujans-number-in-c#

https://stackoverflow.com/questions/32876131/making-hardy-ramanujan-nth-number-finder-more-efficient

http://recmath.org/Magic%20Squares/narciss.htm

https://ia801004.us.archive.org/17/items/martingardnerthecolossalbookofmathematics/Martin%20Gardner%20-%20The%20Colossal%20Book%20Of%20Mathematics.pdf

http://jnsilva.ludicum.org/HMR13_14/536.pdf

https://mathoverflow.net/questions/152580/recreational-mathematics-where-to-search

http://www.science.smith.edu/~jhenle/pleasingmath/

Manuscript and citation

Soumya Banerjee, "Ramanujan Cab Numbers: A Recreational Mathematics Activity," Journal of Humanistic Mathematics, Volume 12 Issue 2 (July 2022), pages 503-517.

Available at:

https://scholarship.claremont.edu/jhm/vol12/iss2/29

Preprint

https://osf.io/a2jc9/

banerjee, soumya. 2022. “Ramanujan Cab Numbers: A Recreational Mathematics Activity.” OSF Preprints. May 10. doi:10.31219/osf.io/a2jc9