Write a function collatzseg (n) which computes the Collatz sequence (as a Python list) given an...

 

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Write a function collatzseg (n) which computes the Collatz sequence (as a Python list) given an initial value n. For example, the output of collatzseq (5) should be [5,16,8,4,2,11 (ii) Write a function collatzcount (n) which counts the number of steps s(n) until the sequence starting at 12 reaches 1. For example, s(1) = 0 and as above s(11) = 14. (iii) Plot a graph of s(n) against n for n € [1, 1000]. Use circles for markers instead of lines. (iv) What percentage of initial values n have the property that s(n) <n/10 for n = [1, 1000]? (Write your answer as a comment, including any code you used to obtain it but commented out.) (v) Let max(n) be the largest integer reached by the sequence with initial value n before ending at 1. That is, max(n) = max(A, | Aon). For example, in the case above, max(11) = 52. Plot a graph of max(n) against n for n E [1, 1000]. Investigate using different plotting techniques such as: restricting the y-axis, logarithmic plots, using a bigger range for x (so long as this doesn't make your code too slow), or plotting additional points or lines to help identify any patterns you can see. Comment on your observations (including your answer as a comment). Write a function collatzseg (n) which computes the Collatz sequence (as a Python list) given an initial value n. For example, the output of collatzseq (5) should be [5,16,8,4,2,11 (ii) Write a function collatzcount (n) which counts the number of steps s(n) until the sequence starting at 12 reaches 1. For example, s(1) = 0 and as above s(11) = 14. (iii) Plot a graph of s(n) against n for n € [1, 1000]. Use circles for markers instead of lines. (iv) What percentage of initial values n have the property that s(n) <n/10 for n = [1, 1000]? (Write your answer as a comment, including any code you used to obtain it but commented out.) (v) Let max(n) be the largest integer reached by the sequence with initial value n before ending at 1. That is, max(n) = max(A, | Aon). For example, in the case above, max(11) = 52. Plot a graph of max(n) against n for n E [1, 1000]. Investigate using different plotting techniques such as: restricting the y-axis, logarithmic plots, using a bigger range for x (so long as this doesn't make your code too slow), or plotting additional points or lines to help identify any patterns you can see. Comment on your observations (including your answer as a comment).

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Heres a Python script that includes the functions described in your question along with code for plo... View the full answer