In the "Collatz conjecture" we want to find a number that makes the process go on forever never reaching 1. I want to find an example - a problem like "Collatz conjecture" but where you have to find a number that makes the process stops (the opposite situation, where you know alot of numbers that makes the process go on forever).
Collatz conjecture - example on the opposite situation
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0I want to find a problem like the collatz conjecture, but where in most cases the sequence doesn't reach a given number, but we haven't proven it yet. – 2011-12-08
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2The question makes sense to me. Here is an illustration to show what something like this could be. Consider the recursion $x \mapsto x/2$ for $x$ even, $x \mapsto 5x+1$ for $x$ odd. Nonrigorous arguments predict that this sequence should go to infinity for most initial conditions. In this case, it is pretty easy to find some loops, for example, $1 \to 6 \to 3 \to 16 \to 8 \to 4 \to 2 \to 1$. But one could imagine a recursion for which the heuristics predict that most values will escape to $\infty$, and for which it is open to find any loops. I think this is what Ilikenumbers wants. – 2011-12-08
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2You might like to look at this answer of mine http://math.stackexchange.com/questions/14569/the-5n1-problem/14590#14590 – 2011-12-08