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Consider the following operation on an arbitrary positive integer:

If the number is divisible by 12, divide it by 12.

If the number is divisible by 10, divide it by 10.

If the number is divisible by 8, divide it by 8.

If the number is divisible by 6, divide it by 6.

If the number is divisible by 4, divide it by 4.

If the number is divisible by 2, divide it by 2.

If the number is odd, multiply it by 5 and add 1.

The tests should be performed in this order.

The conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially.

This can be tested by running this simple python script:

#!/usr/bin/python



for i in range(2,1000):

    x = i

    while x != 1:        

        print "{0}, ".format(x),                       

        if x % 12 == 0:

            x = x / 12

        elif x % 10 == 0:

            x = x / 10

        elif x % 8 == 0:

            x = x / 8

        elif x % 6 == 0:

            x = x / 6

        elif x % 4 == 0:

            x = x / 4

        elif x % 2 == 0:

            x = x / 2

        else: 

            x = 5 * x + 1

    print "n"