I am doing some maths at the moment which is way above my feield of understanding, and if one of you could explain it it would be greatly appreciated.
the project is about this pattern. which is descibed below.
If you get a odd number, you multiply it by 3 and add one. so 3n+1
if you get a even number, you half it.
the sequence ends when you get to one.
so if you started with 3 you would go: 3-10-5-16-8-4-2-1-end
now the realy hard question in this project is this:
I have to prove weather or not there is a number that never reaches one.
here is the question:
"Investigate whether there are any numbers that have an order of infinity. Think about the different ways the sequence could not reach 1. and then try to find a number that has a infinate order or prove that ever sequence reaches 1. You should think about what the smallest number n with infinate order would need to be (for instance, you can tell it cannot be even because then n/2 would be a smaller number with infinite order.) You migfht also like to think about the maximum number reached in any sequence, for example, in a sequence starting with 11, the largest number was 52. Make a note of any patterns you notice if you cannot come up with a complete soulution to the problem.
I have a function written for python which counts the number of steps taken:
I need some help as to how to get started.
Thanks in advance,
4o4found
the project is about this pattern. which is descibed below.
If you get a odd number, you multiply it by 3 and add one. so 3n+1
if you get a even number, you half it.
the sequence ends when you get to one.
so if you started with 3 you would go: 3-10-5-16-8-4-2-1-end
now the realy hard question in this project is this:
I have to prove weather or not there is a number that never reaches one.
here is the question:
"Investigate whether there are any numbers that have an order of infinity. Think about the different ways the sequence could not reach 1. and then try to find a number that has a infinate order or prove that ever sequence reaches 1. You should think about what the smallest number n with infinate order would need to be (for instance, you can tell it cannot be even because then n/2 would be a smaller number with infinite order.) You migfht also like to think about the maximum number reached in any sequence, for example, in a sequence starting with 11, the largest number was 52. Make a note of any patterns you notice if you cannot come up with a complete soulution to the problem.
I have a function written for python which counts the number of steps taken:
Code:
def order(num):
steps=0
while num > 1:
if num % 2 == 0:
num = num / 2
else:
num=num*3+1
steps=steps +1
return stepsI need some help as to how to get started.
Thanks in advance,
4o4found
