This sequence approximates an integer to arbitrary precision, not 8 specifically though, and never perfectly.
I tried it out using other bases, and the rule seems to be that doing this in base n results in n-2 with remainder n-1. So it doesn’t ever actually converge, but the remainder becomes small very fast.
Edit: you can kinda think of it being 0, plus the 1/1 that would have ended up as a remainder in larger bases. In base 2, it just ends up being a full 1.
This sequence approximates an integer to arbitrary precision, not 8 specifically though, and never perfectly.
I tried it out using other bases, and the rule seems to be that doing this in base n results in n-2 with remainder n-1. So it doesn’t ever actually converge, but the remainder becomes small very fast.
eyes you in binary
The sequence in base 2 is only 1/1.
Wonder how close base-16 gets.
FEDCBA987654321 / 123456789ABCDEF
Off by ‘1.82959E–16’ !
Hmmmm…
Edit: you can kinda think of it being 0, plus the 1/1 that would have ended up as a remainder in larger bases. In base 2, it just ends up being a full 1.