4 ms·

Thanks, but there's a bug in your code/results - for example, 1011 does not converge to 0, it does hit 6174 in 5 steps. Only 1111, 2222, etc. yield 0. I suspec

• waterhouse 15y ago
  For 1011, the next step is 1110 - 0111 = 999, and then... apparently you're supposed to handle that as 9990 - 0999, rather than 999 - 999. Huh. I see. But I'm inclined to consider that a bug in the definition, rather than in the code. :-} The four-digit-ness came from applying the operation to four-digit numbers, and saying "oh yeah and we'll zero-extend the results to four digits" introduces an ugly element of redundancy. However, we can make it not ugly anymore by making "zero-extend everything to make it be 4 digits" the primary condition. Instead of applying it to 4-digit numbers, we'll make every number have 4 digits and then apply the Kaprekar procedure. So we'll now be working with the numbers 0000-9999, rather than 1000-9999. (There's no way to zero-extend numbers bigger than 9999 to be 4 digits, so that's all.) Here are the results for 0000-9999: http://pastebin.com/TQ3cMshV http://pastebin.com/TQ3cMshV I think the frequencies of the number of steps to equilibrium are somewhat nicer, as well, when you count 0000-0999. As a simple metric, they have more factors of small primes, especially 2. 1000-9999: 0 steps: 1 = 1 1 steps: 365 = 5 * 73 2 steps: 519 = 3 * 173 3 steps: 2124 = 2^2 * 3^2 * 59 4 steps: 1124 = 2^2 * 281 5 steps: 1379 = 7 * 197 6 steps: 1508 = 2^2 * 13 * 29 7 steps: 1980 = 2^2 * 3^2 * 5 * 11 0000-9999: 0 steps: 2 = 2 1 steps: 392 = 2^3 * 7^2 2 steps: 576 = 2^6 * 3^2 3 steps: 2400 = 2^5 * 3 * 5^2 4 steps: 1272 = 2^3 * 3 * 53 5 steps: 1518 = 2 * 3 * 11 * 23 6 steps: 1656 = 2^3 * 3^2 * 23 7 steps: 2184 = 2^3 * 3 * 7 * 13