Please solve in python!

A hailstone sequence is an infinite sequence that is generated recursively by the following rule: $b_1=S,b_{n+1}=\{\begin{array}{ccc}\frac{1}{2}{b}_n& if{b}_{n}is\text{e}\text{v}\text{e}\text{n}& \\ 3b_n+1& if{b}_{n}is\text{o}\text{d}\text{d}& \end{array}$

where the positive integer S is the seed value. This sequence$$s name is inspired by the behavior of its values, which typically ascend and descend erratically like hailstones in a strong storm.

$($a$)$ Choose any four seed values less than $25$ and print the first $30$ terms of the corresponding

hailstone sequences. Do you notice any patterns in the behavior of these values as each sequence progresses? Print a statement that precisely describes your observations.

$($b$)$ Write a Python function that performs the following tasks:

$$ Accept a seed integer as input.

$$ Print True if the pattern you observed in part $($a$)$ appears within the first $300$ terms of the corresponding hailstone sequence. If not, print False.

$$ If True was printed, also print the number of terms that had to be checked before the

predicted pattern occurred.

Run your function with the seed integers S$=157,1011,3453,5722.$

$($c$)$ Using plt$.$plot$(),$ graph the following partial hailstone sequences.

$($i$)$ S $=103$ with n $88.$

$($ii$)$ S $=385$ with n $33.$

$($iii$)$ S $=512$ with n $10.$

$($iv$)$ S $=1758$ with n $149.$

Note: You may need to use plt$.$show$()$ after each plotting command to separate the graphs into different images.