The Juggler Sequence - Maple Help
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The Juggler Sequence

Main Concept

A juggler sequence is an integer sequence which begins with a positive integer a__0 and has each subsequent term defined by the recursive relation:

 ak=ak12if ak is evenak32if ak is odd  , where x denotes the floor function.

The name of this sequence comes from the rising and falling nature of the terms, which resembles the movement of balls or clubs in the hands of a juggler. After a juggler sequence reaches 1, all subsequent terms equal 1. It is conjectured that all juggler sequences eventually descend to 1, no matter what positive integer they begin with.


Enter a positive integer in the box below and click "Next Term" to find the next term in the juggler sequence. Does your sequence always eventually reach the number 1?

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