Lesson plan
Juggler sequence
In number theory, a juggler sequence is an integer sequence that starts with a positive integer a 0 , with each subsequent term in the sequence defined by the recurrence relation: a_{k+1}= \begin{cases} \left \lfloor {a_k}^{\frac{1}{2}} \right \rfloor, & \text{if } a_k \text{ is even} \\ \\ \left \lfloor {a_k}^{\frac{3}{2}} \right \rfloor, & \text{if } a_k \text{ is odd}. \end{cases}
Article summary
In number theory, a juggler sequence is an integer sequence that starts with a positive integer a 0 , with each subsequent term in the sequence defined by the recurrence relation: a_{k+1}= \begin{cases} \left \lfloor {a_k}^{\frac{1}{2}} \right \rfloor, & \text{if } a_k \text{ is even} \\ \\ \left \lfloor {a_k}^{\frac{3}{2}} \right \rfloor, & \text{if } a_k \text{ is odd}. \end{cases}
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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