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Status Replies posted by John

I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.

I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.

I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.

So you iterate through the natural numbers, and for each natural number N, the equation takes that and outputs all odd numbers whose sequences contain exactly N iterations of the odd rule, along with the powers of 2 involved in traveling from one odd number in the sequence to another?
So for N = 1, we have {1, 5, 21, 85, 341...}, or [(4^n)  1]/3 for all natural numbers n. I'm eager to see how the equation produces/presents its output.


I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.

Yeah, it seemed like the kind of thing you'd have realized fairly quickly, but I decided to simply edit rather than delete just in case. After all, it's easy to miss the trees for the forest sometimes.
So just so I'm clear here, you're developing a formula that, given an odd input c, should generate all the numbers that reduce to 1 using n/2 for evens and cn+1 for odds along the sequence? Or what?


I have finally made a break through on the Collatz conjecture. Although I still cannot prove the conjecture, my work has allowed me to create two new challenges, one which will be the toughest one yet... I'll have them posted as soon as I can find the time to write them up.

The 1n+1 case is trivially true, since (n+1)/2 < n except for the case n = 1. So you can probably take that as given and move on to looking at the relationships between various coefficients.
Edit: Unless you mean you're trying to prove it using the equation you're developing, in which case don't mind me.


How old is science forums?

I just felt like posting something.

I just felt like posting something.

'The Elegant Universe' (Brian Greene). Great book.

So what should I get for an intro to geometry?

A man said, "You're mad." I said, "Mad?" He said, "Yes." I said, "Who?" He said, "You." I said, "Me?" He said, "Yes." I said, "Oh..."