4 ms·
I'll take a stab. An odd number is a number that ends in 1, 3, 5, 7, or 9. - ends in a 1: times 3 + 1: it now ends in a 4, which is even, and thus reduces to
by Beldin 4y ago
I'll take a stab.
An odd number is a number that ends in 1, 3, 5, 7, or 9.
- ends in a 1: times 3 + 1: it now ends in a 4, which is even, and thus reduces to the even case.
- ends in a 3: tomes 3 is 9, + 1: ends in a 0; even again.
- ends in a 5: ×3 ends in a 5 again, +1: ends in a 6; again even!
- ends in 7: x3: now ends in a 1, +1: ends in a 2; even yet again!
- ends in a 9: ×3 then eens in a 7, +1 thus eens in an 8: even again!!
So all that's left is the cases for @someweirdperson ;-) @someweirdperson
- cman1444 4y agoI think this is getting at a pretty good point. Half of all numbers (all evens) will scale by .5 to the subsequent number. The other half (odds) will effectively scale by approximately 3/2, as you have shown here. Obviously over a large amount of iterations this should cause the calculations to trend lower and lower.
- FartyMcFarter 4y agoOne difficulty with this approach is that it doesn't help disproving the existence of cycles, it only makes it less likely that the sequence diverges to infinity.
- linkdd 4y agoAnother approach would be using the "inverse" of the formula and then trying to prove that you can build all natural numbers starting from 1. This approach, like every other approaches, did not yield any significant result. The funny thing is that it fits right in the P=NP problem: easy to verify, hard to solve :)