11348

The 196 Algorithm, Reorder-and-Add Algorithm, and RATS Sequence in Different Bases

This Demonstration presents two well-known algorithms, the 196 algorithm and the RATS sequence (reverse, add to the original, then sort the digits), and a variation, the reorder-and-add algorithm.
The 196 algorithm (or the reverse-and-add algorithm) reverses the digits of a number and adds that to the original number. For example, . It is conjectured that all numbers in base ten that are iterated using this algorithm end up in a palindrome (a number that reads the same from either direction). 196 is the smallest number in base ten that might not result in a palindrome: . Numbers that do not end up in a palindrome are called Lychrel numbers.
The reorder-and-add algorithm reorders the original number by a certain number and adds it back. For example, with , .
The RATS sequence adds an extra step to the 196 algorithm. As before, reverse the number and add it to the original number, but then sort the digits. For example (where "⟶" means reverse and add and "⟹" means sort), .
You can perform these algorithms with any number from 10 to 100,000 in any base from 1 to 10, and you can also represent the numbers in any base from 1 to 10.
The tabs at the top show the three different algorithms. The palindrome checker stops when it reaches a palindrome. You decide how much to iterate the 196 algorithm, the reorder-and-add algorithm, and the RATS sequence. The "number of digits reordered slider" only works for the reorder algorithm.
  • Contributed by: Neel Gandhi
  • (Mathematica Summer Camp 2016)

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+