I would also like to reason out as to why this can be a good poylmath project. Firstly, the problem doesn’t simply fit into a restricted branch of mathematics and thus provides scope for greater participation.

This problem popularized by Martin Gardener, remains unsolved over 40 years probably not just for its difficulty as such but for no reasonable attempts being made.

Clearly, this problem is of computational nature to a certain degree and a wider audience may help progress accelerate.

Call Λ (capital lambda) the function on all positive odd integers which is the result of the iterations of the reduced Collatz function (T) according to the following algorithm : as long as the result is odd, apply T (ascending phase), then : as long as the result is even, apply T (descending phase).

For instance, the iterations of the T function starting at 27 give 41, 62, 31, 47, 71, 107, 161, 242, 121, 182, 91, 137, 206, 103…

So Λ(27)=31, Λ(31)=121, Λ(121)=91, Λ(91)=103… And also for instance Λ(107)=121, obviously. It is a simple extension of the N function of the litterature.

I found that it could be expressed in a single generic formula:

Λ [ 2^(2.3^(i-1) k+i+j+1) n+(2^(2.3^(i-1) k+i+j).((3^i+2)^(3^i-j) mod 2.3^i )+2^i-3^i)/3^i ] = 2.3^i.n+((3^i+2)^(3^i-j) mod 2.3^i )

with n,k∈N, i∈N*, j=1 to 2.3^(i-1)

Note that φ(2.3^i )=2.3^(i-1) (where φ is Euler’s function ; thus the interval of values taken by j) and that (3^i+2) is a primitive root modulo 2.3^i.

Also note that the Λ function on odd positive integers as defined above (1,1,1,13,7,13,5,5,13,11,1…) is not referenced in the OEIS.

Still making research on this function but not sure whether it could help progressing on this problem…

]]>Please join the working group https://www.facebook.com/groups/557060461583665/ for PolyPrize, a crypto alternative to Abel Prize and Nobel Prize. If you are an established scientist, we very much welcome you to become a committee member for deciding who will receive the prizes. See the above URL for more information. Please also post nominations for receiving the prizes (self-nominations are currently accepted).

]]>No need to fund the committee, we will just mint crypto tokens out of nothing using my software (in a prerelease state now). I have created a smart and mathematically beautiful software for minting crypto money out of nothing by committee (“court”) decisions.

For example, mint 1000 tokens for a discovery equivalent to a typical Abel Prize. We should give as many prizes as possible, limited only by the committee volunteering time because we are not limited by an amount of money. We can also accept donations and give prizes in the usual cryptocurrencies, but the main idea is that we mint money ourselves. Our minted money may (I hope) grow in price just like BitCoin (for the same reason as BitCoin, because it is hard to obtain).

For now, when the software is yet in preparation, people who want to be judges, please reply to this comment with your names and short bios. You should also create for yourself an Ethereum wallet (use MetaMask browser plugin) and list it in your comment. You need also to buy a small amount (e.g. equivalent of $5) of Ether cryptocurrency to pay for voting network fees when you start to vote.

We can start judging short afterward. The main issue now is to find enough qualified judges. Please reply below stating that you want to be a judge. It is very important because Abel prize is clearly not enough to cover every significant discovery, we need new prizes. And now we have the opportunity to do it on a low expense.

]]>There is a proposal for one but its too specific towards a method.

]]>Hm one more thought:

If I write my thoughtd in Polymath style (with all negative results, ideas, etc.) it could help me to organize my own thoughts (even if nobody other helps me). Could it really help me to organize my thoughts?

]]>However I am not sure if this makes much sense, because only people who have already read my book can reasonably participate in my research. So I don’t expect that many people will come in nearby time.

I ask your advice whether it is worth my time to attempt to set several Polymath-like projects there.

]]>