1 number of length 0, 9 numbers of length 1 (and maybe 0), 90 numbers of length 2, 900 numbers of length 3, 9000 numbers of length 4
9*10^(n-1) numbers of length n. For each n the amount of numbers of length just before that is 10 times less and the amount of numbers the next length is 10 times more. If you take a rolling fraction of n odd to all numbers seen it starts to go down when even numbered length is reached and starts to go up when an odd length number is reached.
(Ignoring that most people don’t think of 0 as of being length 0.)
Jump by two orders of magnitude every time and it stays stable:
Starting with nothing:
1 of even length, 9 of odd length.
90 of even length, 900 of odd length.
10% versus 90%.
Start after an even jump:
91 of even length, 9 of odd length.
9,091 of even length, 909 of odd length.
(Starts at 91% even, but drops after a double jump. I don’t know what the limit on this is.)
By comparison, resolving proportion of even numbers versus odd numbers, is much easier, because it’s a simple pattern which oscillates at the same rate, instead of changing.
9*10^(n-1) numbers of length n.
(in base 10)
Well, if a different color is used every time, then the coloring aspect is solved. If you ask about addition though, then things get weird.
1 number of length 0, 9 numbers of length 1
(and maybe 0), 90 numbers of length 2, 900 numbers of length 3, 9000 numbers of length 49*10^(n-1) numbers of length n. For each n the amount of numbers of length just before that is 10 times less and the amount of numbers the next length is 10 times more. If you take a rolling fraction of n odd to all numbers seen it starts to go down when even numbered length is reached and starts to go up when an odd length number is reached.
(Ignoring that most people don’t think of 0 as of being length 0.)
Jump by two orders of magnitude every time and it stays stable:
Starting with nothing:
1 of even length, 9 of odd length.
90 of even length, 900 of odd length.
10% versus 90%.
Start after an even jump:
91 of even length, 9 of odd length.
9,091 of even length, 909 of odd length.
(Starts at 91% even, but drops after a double jump. I don’t know what the limit on this is.)
By comparison, resolving proportion of even numbers versus odd numbers, is much easier, because it’s a simple pattern which oscillates at the same rate, instead of changing.
(in base 10)
Well, if a different color is used every time, then the coloring aspect is solved. If you ask about addition though, then things get weird.