Collatz conjecture General forum

2 replies. Last post: 2018-04-16

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Collatz conjecture
  • The_Burglar at 2018-04-16

    for a big odd number (n) the next number could be

    odd, 1/2 chance (3n+1)/2 which is near average 3/2 n

    2*odd, 1/4 chance (3n+1)/4 which is near average 3/4 n

    =3/4 chance sum = near average  =(3/2/2+3/4/4)(4/3) =5/4 n

    4*odd 1/8 chance (3n+1)/8 which is near average 3/8 n

    =7/8 chance sum = near average =(3/2/2+3/4/4+3/8/8)(8/7) = 9/8 n

    expand fully n leads to n on average

    but if it hits lower numbers it will lead to 1

    unless it can increase forever

  • Nimble95 at 2018-04-16

    This looks like an informal argument for the truth of the Collatz conjecture. A fun exercise if you have the time is to attempt a formal proof using mathematical induction. It’s frustrating how provable the conjecture looks, and how impossible producing an actual proof seems...after a few hours of trying :)

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