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Results tagged with collatz-conjecture
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user 6094
The Collatz Conjecture, also known as the 3n+1 conjecture, is a famous open problem named after Lothar Collatz.
19
votes
3
answers
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views
A curious sequence of rationals: finite or infinite?
Consider the following function repeatedly applied to a rational
$r = a/b$ in lowest terms:
$f(a/b) = (a b) / (a + b - 1)$.
So, $f(2/3) = 6/4 = 3/2$. $f(3/2) = 6/4 = 3/2$.
I am wondering if it is pos …
- 151k
17
votes
2
answers
1k
views
Does 53 diverge to infinity in this Collatz-like sequence?
This function has been explored a bit at MSE (in June 2016):
\begin{eqnarray}
f(n) &=& (n-1)^2 \; \textrm{if} \; (n \bmod 4) = 1\\
f(n) &=& \lfloor n/4 \rfloor \; \textrm{otherwise}
\end{eqnarray}
wit …
- 151k
31
votes
4
answers
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views
A Collatz-like function that bifurcates on primes
This is likely piling one mystery on another, but ...
I was exploring a function $f(n): \mathbb{N} \mapsto \mathbb{N}$ defined as follows:
$$
f(n) =
\begin{cases}
n^2 & \text{if} \;n \;\text{is prim …
- 151k