Howdy,
Not sure this will be entirely clear, but when considering the relationship between a start value n in the Collatz algorithm and the length of the sequence generated by n, is there a function f() such that f(n) = y >= length(Collatz(n))?
Howdy, Not sure this will be entirely clear, but when considering the relationship between a start value n in the Collatz algorithm and the length of the sequence generated by n, is there a function f() such that f(n) = y >= length(Collatz(n))? 

closed as not a real question by Ryan Budney, Qiaochu Yuan, Todd Trimble♦, gowers, Steve Huntsman Jun 12 '11 at 23:35It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


The existence of such a function is equivalent to the unproven statement that all n eventually settle into the $4, 2, 1$ cycle. Or do I misunderstand your question? 

