f(n)= 3n+1 n/2 if n is odd if n is even
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Collatz Sequence
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's
problem (after Shizuo Kakutani), the Thwaites conjecture (after Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or
hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.
Mathematics
The Collatz function is defined for a positive integer n as follows.
f(n) = = 3n+1 if n is odd
n/2 if n is even
We consider the repeated application of the Collatz function starting with a given integer n, as follows:
f(n), f(f(n)), f(f(f(n))), ...
It is conjectured that no matter which positive integer n you start from, this sequence eventually will have 1 in it. It has been verified to hold for numbers up to 5 × 260 [Wikipedia: Collatz Conjecture].
If n=7, the sequence is
1. f(7) = 22
2. f(f(7)) = f(22) = 11
3. f(11) = 34
4. f(34) = 17
5. f(17) = 52
6. f(52) = 26
7. f(26) = 13
8. f(13) = 40
9. f(40) = 20
10. f(20) = 10
11. f(10) = 5
12. f(5) = 16
13. f(16) = 8
14. f(8) = 4
15. f(4) = 2
16. f(2)= 1
Thus if you start from n=7, you need to apply f 16 times in order to first get 1.
In this question, you will be given a positive number <= 32,000.
You have to output how many times f has to be applied repeatedly in order to first reach 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9d719ba-e39e-4fe2-8bfa-358c0a92b751%2F778b81ee-a71e-4d76-b566-447979f4cca7%2Ffq78gct_processed.png&w=3840&q=75)
Transcribed Image Text:Collatz Sequence
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's
problem (after Shizuo Kakutani), the Thwaites conjecture (after Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or
hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.
Mathematics
The Collatz function is defined for a positive integer n as follows.
f(n) = = 3n+1 if n is odd
n/2 if n is even
We consider the repeated application of the Collatz function starting with a given integer n, as follows:
f(n), f(f(n)), f(f(f(n))), ...
It is conjectured that no matter which positive integer n you start from, this sequence eventually will have 1 in it. It has been verified to hold for numbers up to 5 × 260 [Wikipedia: Collatz Conjecture].
If n=7, the sequence is
1. f(7) = 22
2. f(f(7)) = f(22) = 11
3. f(11) = 34
4. f(34) = 17
5. f(17) = 52
6. f(52) = 26
7. f(26) = 13
8. f(13) = 40
9. f(40) = 20
10. f(20) = 10
11. f(10) = 5
12. f(5) = 16
13. f(16) = 8
14. f(8) = 4
15. f(4) = 2
16. f(2)= 1
Thus if you start from n=7, you need to apply f 16 times in order to first get 1.
In this question, you will be given a positive number <= 32,000.
You have to output how many times f has to be applied repeatedly in order to first reach 1.
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