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November 23rd, 2016, 02:24 AM   #1
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From: israel

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Collatz Conjecture bounds

Cycle bounds

Collatz Conjecture

I have an update about what I was trying to find for so long.

(I am still kinda stuck with finishing my proof on a few things.)

I think I said when I will find a limit to x by y I will share it

x = number of even values in a cycle
y = number of odd values in a cycle

x<8/9*floor(1.5^y)-y

I know it's really high but it works and is helpful on a few cases.


Last edited by skipjack; November 23rd, 2016 at 08:34 PM.
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May 16th, 2017, 01:00 AM   #2
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anyone with lower bounds??? i think this is the best results

positive cycles:

x = roundup ( y * ln3/ln2 )

negative cycles:

x = rounddown ( y * ln3/ln2 )

(-1,-2)
(1,2,4)
(-5,-14,-7,-20,-10)
(−17,−50,−25,−74,−37,−110,−55,−16 4 ,−82,−41,−122,−61,−182,−91,−272,−1 36,−68,−34)
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