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For a positive integer N, box(N) is defined as N/2 if N is even, and 3N + 1 if N is odd.  What is the value of box(2009) - box(2008)?

 Oct 28, 2020
 #1
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Your question is a major mathematical conjecture, still unsolved, and is called the "Collatz Conjecture".

 

Box(2009), n = 1 after 24 steps

Box(2008), n = 1 after 68 steps. 

 Oct 28, 2020
 #3
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Each term in this question is NOT derived from the previous term so it is not Collatz conjecture.

 

 

"The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1."

Melody  Oct 28, 2020
 #2
avatar+111602 
+1

For a positive integer N, box(N) is defined as N/2 if N is even, and 3N + 1 if N is odd.  What is the value of box(2009) - box(2008)?

 

Why is it not just...

 

box(2008)=1004

box(2009)=3*2009+1 = 6028

 

box(2009-box(2008) = 6028-1004 = 5024

 Oct 28, 2020

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