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Juggler sequence: Difference between revisions
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added some background, another related task, increased font size for the formulæ, added a wiki link to the sequence creator, and split the definition line to an over/under format to highlight the oddness/evenness of "why for".
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m (added some background, another related task, increased font size for the formulæ, added a wiki link to the sequence creator, and split the definition line to an over/under format to highlight the oddness/evenness of "why for".) |
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{{draft task}}
Background of the '''juggler sequence''':
Juggler sequences were publicized by an American mathematician and author [https://en.wikipedia.org/wiki/Clifford_A._Pickover Clifford A. Pickover]. The name of the sequence gets it's name from the similarity of the rising and falling nature of the numbers in the sequences, much like balls in the hands of a juggler.
;Description
A [https://en.wikipedia.org/wiki/Juggler_sequence juggler sequence] is an integer sequence that starts with a positive integer a[0], with each subsequent term in the sequence being defined by the recurrence relation:
<big> a[k + 1] = floor(a[k] ^ 0.5) if k is even <big> ''' ''or'' '''
<big> a[k + 1] = floor(a[k] ^ 1.5) if k is odd </big>
If a juggler sequence reaches 1, then all subsequent terms are equal to 1. This is known to be the case for initial terms up to 1,000,000 but it is not known whether all juggler sequences after that will eventually reach 1.
;Task:
Compute and show here the following statistics for juggler sequences with an initial term of a[n] where n is between '''20''' and '''39''' inclusive:
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<br>
The results can be (partially) verified against the table [https://web.archive.org/web/20091027053243/http://www.geocities.com/hjsmithh/Juggler/JuggWhat.html here].
;Related
* [[Hailstone sequence]]
: [[Yellowstone sequence]]
;See also:
* [[oeis:A007320]] Number of steps needed for Juggler sequence started at n to reach 1
* [[oeis:A094716]] Largest value in the Juggler sequence started at n
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