Say we know that these numbers reach one (which we do):
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Now, obviously, double all these numbers reach one two, so we know:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20 (and more doubles)
If we can figure out a way to find out how the next odd number reaches one (through iterations), then we can fill in the odd numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Now we can double these...etc.
There could be easier ways, but that sequence that I made just looks so uniform that I feel it has to have something...
I still don't understand what your sequence is doing... in particular can you clarify this?
"So if we can find a pattern in how much difference there is from an even number to the next odd number, that means we can keep using that to get all natural numbers. The difference from each even number to the next odd number is this"
The first sentence I just explained earlier in this post, and the second sentence is leading up to the sequence which I say right afterwards.