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Collatz conjecture facts for kids

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Lothar Collatz
German mathematician Lothar Collatz

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. It is about what happens when something is done repeatedly (over and over) starting at some number n:

  • 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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