In this question I was wondering if the $3$ in the Collatz conjecture is arbitrary, and when I wrote that question I tried to change to $7n+1$ starting with the seed number $7$, the sequence appears to exhibit unbounded growth.

To analyze this behavior, I had a Python script developed to simulate the sequence. Remarkably, after $3000$ iterations, the maximum value is about $10^{266}$. This observation leads me to hypothesize that the sequence may either diverge to infinity or enter an extremely lengthy loop.

Here is the code for plotting the first $1000$.

```
import matplotlib.pyplot as plt
import numpy as np
a = 7
xpoints = []
ypoints = []
for i in range(1 , int(1000)):
if a % 2 == 0:
a //= 2
else:
a = a * 7 + 1
xpoints.append(i)
ypoints.append(a)
plt.plot(np.array(xpoints) , np.array(ypoints))
plt.show()
```

Does this sequence diverge to infinity?, and if so, how can we prove it? Alternatively, if the sequence does not diverge, what is the length of its loop?

Given the complexity of this problem, If the problem can't be solved with computational solution for the loop or the proof of divergence already exist then I think this question might be as challenging as solving the original Collatz conjecture .

The question has been asked on MSE here.

exactlywhat algorithm is being discussed, instead of expecting readers to guess correctly or read the code. $\endgroup$You neglected to state clearly in English what your algorithm is.$\endgroup$