/sci/ - Science & Math

If there exists a number that disproves the conjecture, then there exists a smallest number that disproves the conjecture. Therefore, the first number that disproves the conjecture never reaches any number below itself, since these numbers all eventually reach 1.

Instead of testing every single number, we can instead test general forms of numbers to see if that can be possible candidates for the smallest number that disproves the conjecture. We know that even numbers, or 2n, cannot be candidates, since they immediately half and go below their original value. So we first start with the form:

2n + 1
Applying the Collatz process:
2n+ 1 -> 6n + 4
6n + 4 -> 3n + 2

Now at this point, it isn’t known whether 3n + 2 is odd or even, as it depends on what n is. If n is even, then 3n + 2 is even, which means it goes to 1.5n + 1, which is less than the original. So we want to eliminate this possibility by making our original n odd.

So 2n + 1 becomes 2(2n + 1) + 1 = 4n + 3

When we apply the same process as above, we get

4n + 3 -> 12n + 10
12n + 10 -> 6n + 5
18n + 16 -> 9n + 8

Now n cannot be divisible by 4, since then 9n + 8 would be divisible by 4, causing it to drop below 4n + 3. So now we replace 4n + 3 with

4(4n + 1) + 3 = 16n + 7
4(4n + 2) + 3 = 16n + 11
4(4n + 3) + 3 = 16n + 15

And now we have to check these forms also. I’ve been thinking about making a program that would run through this process automatically. What this process does is further specified exactly what numbers can infinitely grow and never reach numbers below themselves. I’m wondering if it’s possible that C in the form an + C grows to infinity, showing that there is no possible number that can be the first to disprove the conjecture. At the very least, this process can be used to efficiently check which numbers follow the conjecture or not. I’ve already written a program that uses large strings of digits with a manual calculation function so that I can check numbers with dozens of digits in them.

How much energy does it take for the body to produce sebum? What molecules are needed? How many are used?

Since using soaps cause you to produce more sebum, how much energy can you save by not using soaps?

>>11159036