User blog comment:P進大好きbot/Elementary Large Number/@comment-30754445-20181118000005/@comment-30754445-20181118013706

Explicit examples are indeed sufficient when you're doing a variation on an already familiar idea (for example, when you create an array notation that behaves like an FGH-clone).

In the case of your function, though, the examples don't tell us much by themselves. It looks vaguely similar to Emlightened's idea of "pink numbers" (which is also an epsilon-0 level function), but the rules by which the numbers go up and down are not at all obvious. I'm especially confounded by the fact that the multiples x1,x3,x5,x7 sometimes go up and sometimes go down.

So what's needed here is an explanation of the general concept behind your function. Give the people here some context, so they will have a chance to understand what the examples mean.

Another thing that may help, is to write your examples in ascending order of the equivalent ordinals. Some numbers (2560, 3072, 6144) seem to be important in your system, and I can only assume they corrsepond to smallish (perhaps even finite) ordinals. Does 2560 correspond to omega? Or does 2560 correspond to "1", 3072 to "2", and 6144 to omega?

BTW you shouldn't try to mimic what "most people" here are doing. Many times, people don't bother with explanations and/or proofs simply because they don't understand the concepts themselves (I still remember all those rediculous posts that "analyze" BMS up to insanely high ordinals by people who don't even know what an OCF is...).