Collatz conjecture

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The Collatz conjecture is a conjecture (an idea which many people think is likely) in mathematics. It is named after Lothar Collatz. He first proposed it in 1937.[1] It is about what happens when something is done repeatedly (over and over) starting at some number n:[1][2]

  • If n is even (divisible by two), n is halved (divide by two = take its half).
  • If n is odd (not divisible by two), n is changed to 3n+1.

The conjecture states that n will always reach one. Here is an example sequence:

  • 9
  • 28 (9 is odd, so we triple it and add one)
  • 14 (28 is even; 14 is half of 28)
  • 7 (14 is even, 7 is its half)
  • 22 (22 = 3 \times 7 + 1)
  • 11
  • 34
  • 17
  • 52
  • 26
  • 13
  • 40
  • 20
  • 10
  • 5
  • 16 (16 is a power of two, so it will lead to 1, halving each time)
  • 8
  • 4
  • 2
  • 1 (after 1 comes 4, 2, 1, 4, 2, 1, etc.)

(oeis:A033479)

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