neelsoumya / ramanujan_number_generator

Generating Ramanujan cab numbers

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

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

or

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

Clone or download the repository

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

Usage

python ramanujan_test_v1.py

R --no-save < analysis.R

Files

• ramanujan_test_v1.py

  • Usage

    nohup python3 ramanujan_test_v1.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

[email protected]

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