Let's define a simple function \$f\$ which takes an integer and produces a list:
\$ f(n) = [g(1),g(2),\dots,g(n)] \\ g(n) = [f(0),f(1),\dots,f(n-1)] \$
We can then calculate the first couple of values for \$f(n)\$:
0 ->
[]
1 ->
[[[]]]
2 ->
[[[]],[[],[[[]]]]]
3 ->
[[[]],[[],[[[]]]],[[],[[[]]],[[[]],[[],[[[]]]]]]]
4 ->
[[[]],[[],[[[]]]],[[],[[[]]],[[[]],[[],[[[]]]]]],[[],[[[]]],[[[]],[[],[[[]]]]],[[[]],[[],[[[]]]],[[],[[[]]],[[[]],[[],[[[]]]]]]]]
And we notice that each one is bigger than the last and has the last list as a prefix to itself.
So we could say that \$f(\infty)\$ is the infinite sequence such that each \$f(n)\$ is the first \$n\$ entries of it.
Now infinite lists of lists of lists ... are a little complicated so instead we will just treat \$f(\infty)\$ as an infinite sequence of opening and closing brackets. The ,
s are redundant so we just omit them. In fact we don't need to even deal with the brackets since there are only two values we can make a binary sequence!
1110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000001...
[[[]][[][[[]]]][[][[[]]][[[]][[][[[]]]]]][[][[[]]][[[]][[][[[]]]]][[[]][[][[[]]]][[][[[]]][[[]][[][[[]]]]]]][...
Task
Your task is to output the binary sequence given by \$f(\infty)\$. You can choose any two distinct values for 1
and 0
. IO otherwise uses sequence defaults. Read the tag wiki for precise info.
This is code-golf so answers will be scored in bytes with the goal being to minimize your source code size.
Test cases
Here's the first 10000 entries
11100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000000110111000111001101110000011100110111000011011100011100110111000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000000110111000111001101110000011100110111000011011100011100110111000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000000000110111000111001101110000011100110111000011011100011100110111000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000110111000111001101110000011100110111000011011100011100110111000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000000110111000111001101110000011100110111000011011100011100110111000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000000011011100011100110111000001110011011100001101110001110011011100000001110011011100001101110001110011011100000011011100011100110111000001110011011100001101110001110011011100000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000001101110001110011011100000111001101110000110111000111001101110000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000000110111000111001101110000011100110111000011011100011100110111000000011100110111000011011100011100110111000000110111000111001101110000011100110111000011011100011100110111000000000111001101110000110111000111001101110000001101110001110011011100000111001101110000110111000111001101110000000011011100011100110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