Collatz conjecture

conjecture in mathematics that, starting with any positive integer n, if one halves it (if even) or triples it and adds one (if odd) and repeats this ad infinitum, then one eventually obtains 1

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 integer 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 .

The conjecture states that if n is positive, n will always reach one. The problem is computationally verified for all numbers below .[3] 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 ()
  • 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)

ReferencesEdit

  1. 1.0 1.1 "Collatz Problem - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2012-01-20.
  2. https://www.jstor.org/pss/2044308
  3. D. Barina. Convergence verification of the Collatz problem. The Journal of Supercomputing, 2020. DOI: 10.1007/s11227-020-03368-x