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-   -   Find Kaprekar's constants and cycles of the Kaprekar mapping of 9-digit to 12-digit numbe in base 12 (https://www.mersenneforum.org/showthread.php?t=25212)

 sweety439 2020-02-11 03:12

Find Kaprekar's constants and cycles of the Kaprekar mapping of 9-digit to 12-digit numbe in base 12

Can someone find all the 9-digit to 12-digit cycles of the [URL="https://en.wikipedia.org/wiki/Kaprekar%27s_routine"]Kaprekar mapping[/URL] in base 12? I cannot find them, since the range is too large, can someone help me? I only have data for base 10 and base 16 to 20 digits, but no base 12, and I myself searched base 12 to 8 digits and find the cycles:

[CODE]

Digit length Cycles Cycle lengths Number of cycles
1 {0} 1 1
2 {00}, {0E, X1, 83, 47, 29, 65} 1, 6 2
3 {000}, {5E6} 1, 1 2
4 {0000}, {3EE8, 8284, 6376}, {4198, 8374, 5287, 6196, 7EE4, 7375} 1, 3, 6 3
5 {00000}, {64E66, 6EEE5}, {83E74} 1, 2, 1 3
6 {000000}, {420X98, X73742, 842874, 642876, 62EE86, 951963, 860X54, X40X72, X82832, 864654}, {65EE56} 1, X, 1 3
7 {0000000}, {841E974, X53E762, 971E943, X64E652, 960EX53, E73E741, X82E832, 984E633, 863E754}, {962E853} 1, 9, 1 3
8 {00000000}, {4210XX98, X9737422, 87428744, 64328876, 652EE866, 961EE953, X8428732, 86528654, 6410XX76, X92EE822, 9980X323, X7646542, 8320X984, X7537642, 8430X874, X5428762, 8630X854, X540X762, X830X832, X8546632, 8520X964, X740X742, X8328832, 86546654}, {873EE744}, {X850X632} 1, 20, 1, 1 4

[/CODE]

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