News for hackers. Stuff that matters.
Re:6174 by krick on Tuesday January 16, 2024 @07:38PM (#39021443)
Yes at all. 6174 is specific to base-10 and 4 digits. For 4 digit numerals in base-9 there are 2 cycles. Same for 4 digit numerals in base-8. It's unlikely that there's any special meaning for 4-digit numbers in base-10 having a single cycle of length 1, but even if there is (possibility which I cannot just deny, of course) — it doesn't translate to other bases.

So, yes, the described "special" thing about 6174 is actually a special thing about the string 6174 (representing a number in base-10). And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit. People kinda mix up properties of numbers and properties of some other mathematical objects — like their representations in base-10. Most of numerological games are concerned with the latter. Which is why it's especially interesting, when something like that happens to hold in other bases, which sadly just isn't the case with Kaprekar's constant.

Re:6174 by dbrueck on Tuesday January 16, 2024 @09:37PM (#39022525)
Hehe, to me these contrarian comments are strongly reinforcing my point about overzealous pedantry. :) Of course the specific string '6174' is specific to base 10, but the idea itself can be applied to other bases.

Here are some additional examples:

  dec, 3 digits: 495
  hex, 3 digits: 7F8
  hex, 30 digits: EECCAA88664421FFDDBB9977553312
  dec, 30 digits: 988766544332209987766554332111
  hex, 100 digits: FFFFEEEEDDCCCCBBAAAA9998888776666554444333222210FFFFEEDDDDCCCBBBBAA999988777766655554433332211110001
  dec, 100 digits: 9999998888888877666666665544444444332222222210999999998877777777665555555544333333332211111111000001
Whether or not things settle on a single number, the number of loops that exist, etc. are a function of the base and the number of desired digits, but in the cases where inputs do settle on a specific number, there are patterns that emerge (regardless of the base) as the number of digits go up.
Re:6174 by codeflo on Wednesday January 17, 2024 @03:34AM (#39024948)
> And I'd say the fact so many people in this very thread don't understand it is exactly the proof that the GPs comment actually has some merit.

Finally someone noticed the irony, thank you.

(On the other hand, at least some people also criticize my tone rather than the point I'm making, which I guess is fair as well.)