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Topic: More hailstone numbers (Read 1530 times) 

JocK
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More hailstone numbers
« on: Jun 25^{th}, 2005, 8:42am » 
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Starting from a positive integer k, one can generate a series of integers by iterating the mapping: k' = k/2 if k even, k' = (3k+5n)/2 if k odd. Here, n is an odd positive integer constant. Can you find a starting value and a nvalue for which the iteration fails to yield a value not exceeding 347n?

« Last Edit: Jun 25^{th}, 2005, 8:43am by JocK » 
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
x^{y}  y = x^{5}  y^{4}  y^{3} = 20; x>0, y>0.



Barukh
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Re: More hailstone numbers
« Reply #1 on: Jun 26^{th}, 2005, 11:43pm » 
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hidden:  The minimal solution I've found is: n = 29, k = 12655. It generates a 66long cycle with minimal element 19055. Of course, this was achieved using computing power. Currently, I have no idea how to tackle this problem more intelligently. 


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