- Ramanraj K
26 th August, 2020
The results of Kaprekar's operation on 8 digit numbers, are summarised below:
| Constant | Loop size | Frequency | Loop sequence |
|---|---|---|---|
| 86526432 | 3 | 39699019 | 64308654, 83208762, 86526432 |
| 86308632 | 7 | 26158657 | 86326632, 64326654, 43208766, 85317642, 75308643, 84308652, 86308632 |
| 86326632 | 7 | 12696822 | 64326654, 43208766, 85317642, 75308643, 84308652, 86308632, 86326632 |
| 64308654 | 3 | 5452587 | 83208762, 86526432, 64308654 |
| 84308652 | 7 | 3691916 | 86308632, 86326632, 64326654, 43208766, 85317642, 75308643, 84308652 |
| 83208762 | 3 | 3090720 | 86526432, 64308654, 83208762 |
| 85317642 | 7 | 2562102 | 75308643, 84308652, 86308632, 86326632, 64326654, 43208766, 85317642 |
| 75308643 | 7 | 2406872 | 84308652, 86308632, 86326632, 64326654, 43208766, 85317642, 75308643 |
| 64326654 | 7 | 748710 | 43208766, 85317642, 75308643, 84308652, 86308632, 86326632, 64326654 |
| 43208766 | 7 | 512280 | 85317642, 75308643, 84308652, 86308632, 86326632, 64326654, 43208766 |
| 97508421 | 1 | 2370896 | 97508421 |
| 63317664 | 1 | 599410 | 63317664 |
| 00000000 | 0 | 9 | 00000000 |
| Constant | Loop size | Frequency of steps encountered before entering loop | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | ||
| 86526432 | 3 | 268776 | 2264496 | 2077432 | 1360656 | 1512176 | 1725024 | 2112222 | 2126684 | 3013806 | 3224124 | 2619154 | 4484518 | 4048104 | 1952942 | 2076046 | 1281120 | 1802767 | 1745618 | 3354 |
| 86308632 | 7 | 913896 | 3588312 | 5909792 | 5022660 | 2931136 | 1069653 | 896682 | 1241400 | 807636 | 534168 | 816726 | 2130896 | 72316 | 214710 | 8674 | ||||
| 86326632 | 7 | 104148 | 782808 | 492652 | 461604 | 290562 | 826724 | 1043650 | 1062206 | 1763838 | 1517010 | 796756 | 445962 | 963092 | 1614966 | 530844 | ||||
| 64308654 | 3 | 537576 | 1841136 | 1687688 | 1386187 | |||||||||||||||
| 84308652 | 7 | 564456 | 2173776 | 898380 | 55304 | |||||||||||||||
| 83208762 | 3 | 322536 | 1073424 | 558384 | 1106148 | 30228 | ||||||||||||||
| 85317642 | 7 | 430056 | 727120 | 1058936 | 345990 | |||||||||||||||
| 75308643 | 7 | 887016 | 1263288 | 256568 | ||||||||||||||||
| 64326654 | 7 | 47028 | 569452 | 132230 | ||||||||||||||||
| 43208766 | 7 | 161256 | 298962 | 52062 | ||||||||||||||||
| 97508421 | 1 | 604776 | 1505208 | 260912 | ||||||||||||||||
| 63317664 | 1 | 69428 | 198196 | 308278 | 23508 | |||||||||||||||
| 00000000 | 0 | 9 | ||||||||||||||||||