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katadromes
A number whose digits are in strict descending order. more

The first 600 katadromes :
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 210, 310, 320, 321, 410, 420, 421, 430, 431, 432, 510, 520, 521, 530, 531, 532, 540, 541, 542, 543, 610, 620, 621, 630, 631, 632, 640, 641, 642, 643, 650, 651, 652, 653, 654, 710, 720, 721, 730, 731, 732, 740, 741, 742, 743, 750, 751, 752, 753, 754, 760, 761, 762, 763, 764, 765, 810, 820, 821, 830, 831, 832, 840, 841, 842, 843, 850, 851, 852, 853, 854, 860, 861, 862, 863, 864, 865, 870, 871, 872, 873, 874, 875, 876, 910, 920, 921, 930, 931, 932, 940, 941, 942, 943, 950, 951, 952, 953, 954, 960, 961, 962, 963, 964, 965, 970, 971, 972, 973, 974, 975, 976, 980, 981, 982, 983, 984, 985, 986, 987, 3210, 4210, 4310, 4320, 4321, 5210, 5310, 5320, 5321, 5410, 5420, 5421, 5430, 5431, 5432, 6210, 6310, 6320, 6321, 6410, 6420, 6421, 6430, 6431, 6432, 6510, 6520, 6521, 6530, 6531, 6532, 6540, 6541, 6542, 6543, 7210, 7310, 7320, 7321, 7410, 7420, 7421, 7430, 7431, 7432, 7510, 7520, 7521, 7530, 7531, 7532, 7540, 7541, 7542, 7543, 7610, 7620, 7621, 7630, 7631, 7632, 7640, 7641, 7642, 7643, 7650, 7651, 7652, 7653, 7654, 8210, 8310, 8320, 8321, 8410, 8420, 8421, 8430, 8431, 8432, 8510, 8520, 8521, 8530, 8531, 8532, 8540, 8541, 8542, 8543, 8610, 8620, 8621, 8630, 8631, 8632, 8640, 8641, 8642, 8643, 8650, 8651, 8652, 8653, 8654, 8710, 8720, 8721, 8730, 8731, 8732, 8740, 8741, 8742, 8743, 8750, 8751, 8752, 8753, 8754, 8760, 8761, 8762, 8763, 8764, 8765, 9210, 9310, 9320, 9321, 9410, 9420, 9421, 9430, 9431, 9432, 9510, 9520, 9521, 9530, 9531, 9532, 9540, 9541, 9542, 9543, 9610, 9620, 9621, 9630, 9631, 9632, 9640, 9641, 9642, 9643, 9650, 9651, 9652, 9653, 9654, 9710, 9720, 9721, 9730, 9731, 9732, 9740, 9741, 9742, 9743, 9750, 9751, 9752, 9753, 9754, 9760, 9761, 9762, 9763, 9764, 9765, 9810, 9820, 9821, 9830, 9831, 9832, 9840, 9841, 9842, 9843, 9850, 9851, 9852, 9853, 9854, 9860, 9861, 9862, 9863, 9864, 9865, 9870, 9871, 9872, 9873, 9874, 9875, 9876, 43210, 53210, 54210, 54310, 54320, 54321, 63210, 64210, 64310, 64320, 64321, 65210, 65310, 65320, 65321, 65410, 65420, 65421, 65430, 65431, 65432, 73210, 74210, 74310, 74320, 74321, 75210, 75310, 75320, 75321, 75410, 75420, 75421, 75430, 75431, 75432, 76210, 76310, 76320, 76321, 76410, 76420, 76421, 76430, 76431, 76432, 76510, 76520, 76521, 76530, 76531, 76532, 76540, 76541, 76542, 76543, 83210, 84210, 84310, 84320, 84321, 85210, 85310, 85320, 85321, 85410, 85420, 85421, 85430, 85431, 85432, 86210, 86310, 86320, 86321, 86410, 86420, 86421, 86430, 86431, 86432, 86510, 86520, 86521, 86530, 86531, 86532, 86540, 86541, 86542, 86543, 87210, 87310, 87320, 87321, 87410, 87420, 87421, 87430, 87431, 87432, 87510, 87520, 87521, 87530, 87531, 87532, 87540, 87541, 87542, 87543, 87610, 87620, 87621, 87630, 87631, 87632, 87640, 87641, 87642, 87643, 87650, 87651, 87652, 87653, 87654, 93210, 94210, 94310, 94320, 94321, 95210, 95310, 95320, 95321, 95410, 95420, 95421, 95430, 95431, 95432, 96210, 96310, 96320, 96321, 96410, 96420, 96421, 96430, 96431, 96432, 96510, 96520, 96521, 96530, 96531, 96532, 96540, 96541, 96542, 96543, 97210, 97310, 97320, 97321, 97410, 97420, 97421, 97430, 97431, 97432, 97510, 97520, 97521, 97530, 97531, 97532, 97540, 97541, 97542, 97543, 97610, 97620, 97621, 97630, 97631, 97632, 97640, 97641, 97642, 97643, 97650, 97651, 97652, 97653, 97654, 98210, 98310, 98320, 98321, 98410, 98420, 98421, 98430, 98431, 98432, 98510, 98520, 98521, 98530, 98531, 98532, 98540, 98541, 98542, 98543.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1022 values, from 1 to 9876543210).

n\r 0  1 
2681341 2 
3350336336 3 
4272205409136 4 
55272641326633 5 
6231114228119222108 6 
7142145149148146146146 7 
8160117233561128817680 8 
9118112112116112112116112112 9 
105112561286432168421 10 
1109379316221021016293379

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.