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what is Collatz conjecture?
Is Collatz conjecture always true?
What so special about 3x+1 ? ​

Sagot :

jcherry99

Answer:

Step-by-step explanation:

The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.

Simply put it says

  • if a number is even, divide by 2
  • If a number is odd, multiply by 3 and add1. or 3x + 1
  • The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.

Try 5

  • It's odd so triple it and add 1. You get 16
  • 16 is even. Divide by 2. You get 8
  • 8 is even. Divide by 2. You get 4
  • 4 is even. Divide by 2. You get 2
  • 2 is even. Divide by 2. You get 1
  • 1 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.

Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.

  • Take 15
  • It's odd. Triple it and add 1. That gives 46.
  • 46 is even. Divide by 2
  • 23 which is odd. Triple it and add 1  = 70
  • 70 is even. Divide by 2. 35
  • 35 is odd. Triple and add 1.  106  which is even
  • 53 which is odd.  Triple it and add 1. You get 160
  • 160 is even. Divide by 2. You get 80
  • 80 is even Divide by 2. You get 40
  • 40 is even. Divide by 2. You get 20
  • 20 is even. Divide by 2. You get 10
  • 10 is even. Divide by 2. You get 5
  • 5 is odd. Triple it and add 1. You get 16
  • 16 is even. Divide by 2. You get 8
  • 8 is even. Divide by 2. You get 4
  • 4 is even. Divide by 2.. You get 2.
  • 2 is even. Divide by 2. You get 1
  • 1 is odd and you are in the loop because you get 4 which you have already done.

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