Question

IN PYTHON

1.Choose a positive integer

2. To get the next number in the sequence we do the following: If the integer is odd, we multiply by 3 and add 1. If the integer is even, we divide by 2. It is hypothesized that the above sequence will always converge to the value of 1, regardless of any valid initial choice. This hypothesis is known as the Collatz Conjecture. For example, if we start at 5, the numbers generated by the sequence are 16, 8, 4, 2, 1. If we start at 6, the numbers in the sequence are 6, 3, 10, 5, 16, 8, 4, 2, 1.

For this problem, you have to write a program that does the following:

1. Prompt the user for a positive integer. You must ensure the number is positive. However if the user enters the number 0, you should exit the program instead of prompting again.

2. After receiving a valid input, you should iterate through the sequence, keeping track of the number of steps taken until you reach 1 (you may assume the sequence will always converge to 1 for the purpose of this problem). Print out the number of steps taken to reach convergence. Also print out both the largest and second largest values encountered along with their respective step numbers.

1 Please enter a positive integer: -2 2 Please enter a positive integer: 8 3 It took 3 steps for the sequence to reach 1. 4 The largest number in the sequence was 8 (step = 0). 5 The second largest number was 4 (step = 1). =============================== RESTART: Shell =============================== 7 8 9 10 Please enter a positive integer: 5 It took 5 steps for the sequence to reach 1. The largest number in the sequence was 16 (step = 1). The second largest number was 8 (step = 2). ===================EEEEEEEEEEE RESTART: Shell E s sesses EEEEEEEEEEE 12 14 15 16 Please enter a positive integer: 0 ======= RESTART: Shell ====== Please enter a positive integer: 1 The largest number in the sequence was 1 (step = 0). The second largest number was 1 (step = 0).

Answer 1

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this code is meant for python3+

#---------------------INPUT/OUTPUT---------------------------

#----------------------------------------------------------------------

please enter a positive integer: -2 please enter a positive integer: 8 It took 3 steps for the sequence to reach 1. The largest number in the sequence was 8 (step = 0) The second largest number in the sequence was 4 (step = 1 )

#initalizing num

num=-1

#loops until a valid number is entered

while(num<0):

    num=int(input("please enter a positive integer: "))

#to store number of steps

steps=0

#to store steps to get to the largeset num

step_largest=0

#initializing to input number

largest_num=num

#deafult value

second_largest=1

#deafult step

step_second_largest=0

#loops until num does not convergest to 1 given that num was greater than 0 to begin with

while(num!=1 and num>0):

    #incremtn step

    steps=steps+1

    #follow the formula

    if(num%2==1):

        num=num*3+1

    elif(num%2==0):

        num=num//2

    #to compare current num to largest num

    if(largest_num<num):

        largest_num=num

        step_largest=steps

    

    if(second_largest<num and num<largest_num):

        second_largest=num

        step_second_largest=steps

#checks if converged

if(num==1):

    #prints if it took steps

    if(steps!=0):

        print("It took",steps,"steps for the sequence to reach 1.")

    print("The largest number in the sequence was",largest_num,"(step =",step_largest,")")

    print("The second largest number in the sequence was",second_largest,"(step =",step_second_largest,")")

#----------------------------------------------------------------------------

i #initalizing num num=-1 #loops until a valid number is entered while(num<0): num=int(input("please enter a positive integer: ")) 10 11 14 #to store number of steps steps=0 #to store steps to get to the largeset num step largest=0 #initializing to input number largest_num=num #deafult value second largest=1 #deatult step step_second_largest=0 #loops until num does not convergest to 1 given that num was greater than to begin with while(num!=l and num>0): #incremtn step steps=steps+1 #follow the formula if(num%2==1): num=num*3+1 elif (num%2==0): num=num//2 #to compare current num to largest num if(largest num<num):

#-----

largest_num=num step_largest=steps if(second largest<num and num_largest num): second largest=num step_second_largest=steps #checks if converged if(num==1): #prints if it took steps if(steps !=0): print("It took", steps, "steps for the sequence to reach 1.") print("The largest number in the sequence was", largest_num,"(step=", step largest, ")") print("The second largest number in the sequence was", second largest,"(step=", step second largest,")")