
Number Sequences and Base System Patterns
Hard
What happens when you write a number sequence in a different base system and then read the digits as if they were base-10? Surprising patterns appear. Many of these patterns connect back to the original sequence.
You take the first thirty terms of figurate number sequences. Then you translate each term into bases 2 through 20 using a spreadsheet. You read the translated digits as base-10 numbers and scan the results for repeating patterns.
Twenty different patterns emerge across the bases. Most relate to the sequences that created them. Some patterns even connect sequences that seem unrelated at first.
Hypothesis
The hypothesis is that patterns will be found related to the original sequences.
Method & Materials
You will enter the sequences into the spreadsheet, creating a chart for each sequence and its translations from base-2 through 20. You will then scan the chart for patterns formed across many or all of the base systems.
You will need an iMac AppleWorks spreadsheet application's base translator, pencil, and paper.
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See what’s includedResults
Through this project, you'll discover twenty different patterns that demonstrate connections between bases. Most of the patterns created are related to the sequences that created them, and many patterns are related to each other even when the sequences that created them are different.
Why do this project?
This project is unique because it explores the mathematical relationships between number sequences and patterns formed by their translation into multiple base systems.
Also Consider
Experiment variations to consider include translating longer or more complex sequences into higher bases and/or using a computer program to search for patterns.
Full project details
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