I've had no takers, so here's a big hint:
Does it arise "naturally" from something interesting? It has a little of the flavour of the Thue–Morse sequence, which turns up in lots of places.
@ColinTheMathmo it didn't for me - it was inspired by seeing a sentence along the lines of "for each natural number, you have infinitely many balls", and thinking about how you'd stuff infinitely many copies of the natural numbers together
@christianp Huh. I'd do a tighter interleaving, rather than 2 of each, then 4 of each, etc., but I can see how it arises from that.
Is it in the OEIS?
Should it be in the OEIS?
It's very ... parameterisable(?), so maybe not.
@ColinTheMathmo it's not in the OEIS. I was thinking earlier today about how you could make it tighter. Lots of reasonable-looking options end up producing infinite strings of 1s! But there's defo a way of packing them that puts the 1s closer togethee
The first iteration step of your weave is in the OEIS though: https://oeis.org/A009947
I find it slightly more natural to start your power-of-2 weave one position earlier, even though it looks funny with all the doublets. 1,1,2,2,1,3,3,4,1,4,1,5,5,6,6,2,1,7,1,7,8,8,2,9,9,... (This one isn't in the OEIS either.)
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