3 ms·
If you follow the link in the second paragraph to https://en.wikipedia.org/wiki/Kaprekar%27s_routine https://en.wikipedia.org/wiki/Kaprekar%27s_routine, there a
by majewsky 3y ago
If you follow the link in the second paragraph to https://en.wikipedia.org/wiki/Kaprekar%27s_routine https://en.wikipedia.org/wiki/Kaprekar%27s_routine, there are some statements on how this routine plays out in different bases. For base 8, there is no fixed point with 4 digits (i.e. any number that immediately loops back to itself), but apparently there are some cycles (e.g. 3065 → 6152 → 5243 → 3065).
- gweinberg 3y agoSo that means it pretty meaningless, right? The procedure has to yield cycles, and in some bases with some numbers of digit lengths you always get the same cycle of length one, and in others you don't.
- krick 3y agoYep, seems to be so. I mean, it shouldn't be very surprising that among all possible lengths and bases there are some of length 1, would be more astonishing if there wasn't any. But it's not like it's somehow less worthy than other mathematical games. After all, there could have been some meaningful property hidden in there. Doesn't appear so in this case, but you'd never know beforehand.