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f(n)= 3n+1 n/2 if n is odd if n is even

f(n)= 3n+1 n/2 if n is odd if n is even

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
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.
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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