Have a look at this problem:
http://www.programming-challenges.com/pg.php?page=downloadproblem&probid=110101&format=html

In short, you need to calculate the maximum cycle length in a given range.

Roger wrote an essay which is related to this problem.
http://www.jsoftware.com/jwiki/Essays/Collatz_Conjecture

Suppose we want to calculate the maximum cycle length of collatz
sequences for 1, ..., 1e6.

It would be defined, using Roger's definition, as >./ cn 1e6

It currently takes around 40 secs on the computer I'm using. Could you
improve its efficiency?
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