1. xa (mod n) means that when x is divided by n, the remainder is a. Question: Let xo be a positive integer. Xi+1 is defined by the following recurrence relation. x14 if x = 0 (mod 4) (3x+1)/4 ifx, = 1 (mod 4) = i+1 if x = 2 (mod 4) x12 (3x+1)/2 ifx, = 3 (mod 4) The Collatz conjecture is that this process will eventually reach 1. Write a function named £ that finds the least n such that x == 1, given the initial value xo. For example, if xo is 1, the least n is 0. (x0:1) if xo is 2, the least n is 1. (x0:2→x1:1) if xo is 3, the least n is 3. (x0:3→x1:5→ X2:4 → X3:1) if xo is 4, the least n is 1. (x0:4→X1:1) if xo is 5, the least n is 2. (x0:5x1:4 → X2:1) if xo is 6, the least n is 4. (x0:6x1:3→x2:5x3:4x4:1) V if xo is 7, the least n is 7. (x0:7→x1:11x2:17→x3:13 →x4:10→x5:5→X6:4→X7:1) What is f(55)? Write a single number.
1. xa (mod n) means that when x is divided by n, the remainder is a. Question: Let xo be a positive integer. Xi+1 is defined by the following recurrence relation. x14 if x = 0 (mod 4) (3x+1)/4 ifx, = 1 (mod 4) = i+1 if x = 2 (mod 4) x12 (3x+1)/2 ifx, = 3 (mod 4) The Collatz conjecture is that this process will eventually reach 1. Write a function named £ that finds the least n such that x == 1, given the initial value xo. For example, if xo is 1, the least n is 0. (x0:1) if xo is 2, the least n is 1. (x0:2→x1:1) if xo is 3, the least n is 3. (x0:3→x1:5→ X2:4 → X3:1) if xo is 4, the least n is 1. (x0:4→X1:1) if xo is 5, the least n is 2. (x0:5x1:4 → X2:1) if xo is 6, the least n is 4. (x0:6x1:3→x2:5x3:4x4:1) V if xo is 7, the least n is 7. (x0:7→x1:11x2:17→x3:13 →x4:10→x5:5→X6:4→X7:1) What is f(55)? Write a single number.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Transcribed Image Text:1. xa (mod n) means that when x is divided by n, the remainder is a.
Question:
Let xo be a positive integer.
Xi+1 is defined by the following recurrence relation.
x14
if x = 0 (mod 4)
(3x+1)/4
ifx, = 1 (mod 4)
=
i+1
if x = 2 (mod 4)
x12
(3x+1)/2 ifx, = 3 (mod 4)
The Collatz conjecture is that this process will eventually reach 1.
Write a function named £ that finds the least n such that x == 1, given the initial value xo.
For example,
if xo is 1, the least n is 0. (x0:1)
if xo is 2, the least n is 1. (x0:2→x1:1)
if xo is 3, the least n is 3. (x0:3→x1:5→ X2:4 → X3:1)
if xo is 4, the least n is 1. (x0:4→X1:1)
if xo is 5, the least n is 2. (x0:5x1:4 → X2:1)
if xo is 6, the least n is 4. (x0:6x1:3→x2:5x3:4x4:1)
V
if xo is 7, the least n is 7. (x0:7→x1:11x2:17→x3:13 →x4:10→x5:5→X6:4→X7:1)
What is f(55)? Write a single number.
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