# Tagged Questions

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### a Problem about Sequence [duplicate]

Let $a_1$ be an integer. Then we assume $$a_{n+1} = \begin{cases} 3a_n+1,&\text{a_n is odd}\\ \frac{a_n}{2},&\text{a_n is even} \end{cases}$$ Now we prove that for any ...
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### Where can I find out more on Collatz-conjecture like sequences?

I'm interested in Collatz-conjecture (the 3n+1 problem) like sequences. I'm interested in any literature that contains information about problems that are divided into similar cases. I'm ...
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### Longest known sequence of identical consecutive Collatz sequence lengths?

I've just written a simple java program to print out the length of a Collatz sequence, and found something I find remarkable: Consecutive sequences of identical Collatz sequence lengths. Here is some ...
The Collatz Conjecture is well known with the sequence $$f(n) = \begin{cases} n/2 &;\text{if } n \equiv 0 \pmod{2}\\ k\,n+1 &; \text{if } n\equiv 1 \pmod{2} \end{cases}$$ and $k=3$; the ...
$n$,$k$, $m$, $u$ $\in$ $\Bbb N$; Let's see the following sequence: $x_0=n$; $x_m=3x_{m-1}+1$. I am afraid I am a complete noob, but I cannot (dis)prove that the following implies the ...