# Questions tagged [collatz]

for questions about the iterated map $n \to 3n+1$ if $n$ is odd and $n \to \frac n2$ if $n$ is even, and its generalizations to $n \to pn+q$ .

285 questions
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### Cycles in bit-limited verson of Collatz map

By 'bit-limited', I mean that we have a computer/calculator that handles binary numbers up to $n$ bits ($n>=1$), and any numbers greater than $2^n-1$ overflow by truncating the higher bits. ...
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### Polynomial divided by a monomial in some extended Collatz Shortcut function

Quirks of the Collatz shortcut function. One example and some basic questions. The functions here are defined as: $$C_d(n):\mathbb{Z^+}\rightarrow\mathbb{Z^+}$$ $$n\in\mathbb{Z^+}$$ The definition ...
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### When given a non-multiple of $3$, $k$, is it possible construct $m<k$ with these conditions? [closed]

This is another Collatz-related problem about trying to represent a number in a certain form. As is usually the case with the Collatz conjecture, this is probably not useful. My question is : Can ...
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### How do I define an appropriate diameter operator?

I've distilled the Collatz conjecture to this, and I need to understand the next step which is to think about how to correctly define a $\operatorname{diam}$ operator with the desired properties. I ...
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### Particular base-10 digit patterns in Collatz

Note: I will use the abbreviation RCF for the Reduced Collatz Function. The arrangement of certain specific digits produce a particular pattern on the next iteration of the Reduced Collatz Function. ...
### What's the closure of the equivalence classes of numbers the same distance from $\langle2\rangle$ by the Collatz graph?
What's the closure of the equivalence classes of numbers the same distance from $\langle2\rangle$ by the Collatz graph? Let the Collatz function be $f(x)=3x+2^{\nu_2(x)}$ The Collatz conjecture ...