A number whose digits are in nonincreasing order. more
The first 600 nialpdromes :
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
20,
21,
22,
30,
31,
32,
33,
40,
41,
42,
43,
44,
50,
51,
52,
53,
54,
55,
60,
61,
62,
63,
64,
65,
66,
70,
71,
72,
73,
74,
75,
76,
77,
80,
81,
82,
83,
84,
85,
86,
87,
88,
90,
91,
92,
93,
94,
95,
96,
97,
98,
99,
100,
110,
111,
200,
210,
211,
220,
221,
222,
300,
310,
311,
320,
321,
322,
330,
331,
332,
333,
400,
410,
411,
420,
421,
422,
430,
431,
432,
433,
440,
441,
442,
443,
444,
500,
510,
511,
520,
521,
522,
530,
531,
532,
533,
540,
541,
542,
543,
544,
550,
551,
552,
553,
554,
555,
600,
610,
611,
620,
621,
622,
630,
631,
632,
633,
640,
641,
642,
643,
644,
650,
651,
652,
653,
654,
655,
660,
661,
662,
663,
664,
665,
666,
700,
710,
711,
720,
721,
722,
730,
731,
732,
733,
740,
741,
742,
743,
744,
750,
751,
752,
753,
754,
755,
760,
761,
762,
763,
764,
765,
766,
770,
771,
772,
773,
774,
775,
776,
777,
800,
810,
811,
820,
821,
822,
830,
831,
832,
833,
840,
841,
842,
843,
844,
850,
851,
852,
853,
854,
855,
860,
861,
862,
863,
864,
865,
866,
870,
871,
872,
873,
874,
875,
876,
877,
880,
881,
882,
883,
884,
885,
886,
887,
888,
900,
910,
911,
920,
921,
922,
930,
931,
932,
933,
940,
941,
942,
943,
944,
950,
951,
952,
953,
954,
955,
960,
961,
962,
963,
964,
965,
966,
970,
971,
972,
973,
974,
975,
976,
977,
980,
981,
982,
983,
984,
985,
986,
987,
988,
990,
991,
992,
993,
994,
995,
996,
997,
998,
999,
1000,
1100,
1110,
1111,
2000,
2100,
2110,
2111,
2200,
2210,
2211,
2220,
2221,
2222,
3000,
3100,
3110,
3111,
3200,
3210,
3211,
3220,
3221,
3222,
3300,
3310,
3311,
3320,
3321,
3322,
3330,
3331,
3332,
3333,
4000,
4100,
4110,
4111,
4200,
4210,
4211,
4220,
4221,
4222,
4300,
4310,
4311,
4320,
4321,
4322,
4330,
4331,
4332,
4333,
4400,
4410,
4411,
4420,
4421,
4422,
4430,
4431,
4432,
4433,
4440,
4441,
4442,
4443,
4444,
5000,
5100,
5110,
5111,
5200,
5210,
5211,
5220,
5221,
5222,
5300,
5310,
5311,
5320,
5321,
5322,
5330,
5331,
5332,
5333,
5400,
5410,
5411,
5420,
5421,
5422,
5430,
5431,
5432,
5433,
5440,
5441,
5442,
5443,
5444,
5500,
5510,
5511,
5520,
5521,
5522,
5530,
5531,
5532,
5533,
5540,
5541,
5542,
5543,
5544,
5550,
5551,
5552,
5553,
5554,
5555,
6000,
6100,
6110,
6111,
6200,
6210,
6211,
6220,
6221,
6222,
6300,
6310,
6311,
6320,
6321,
6322,
6330,
6331,
6332,
6333,
6400,
6410,
6411,
6420,
6421,
6422,
6430,
6431,
6432,
6433,
6440,
6441,
6442,
6443,
6444,
6500,
6510,
6511,
6520,
6521,
6522,
6530,
6531,
6532,
6533,
6540,
6541,
6542,
6543,
6544,
6550,
6551,
6552,
6553,
6554,
6555,
6600,
6610,
6611,
6620,
6621,
6622,
6630,
6631,
6632,
6633,
6640,
6641,
6642,
6643,
6644,
6650,
6651,
6652,
6653,
6654,
6655,
6660,
6661,
6662,
6663,
6664,
6665,
6666,
7000,
7100,
7110,
7111,
7200,
7210,
7211,
7220,
7221,
7222,
7300,
7310,
7311,
7320,
7321,
7322,
7330,
7331,
7332,
7333,
7400,
7410,
7411,
7420,
7421,
7422,
7430,
7431,
7432,
7433,
7440,
7441,
7442,
7443,
7444,
7500,
7510,
7511,
7520,
7521,
7522,
7530,
7531,
7532,
7533,
7540,
7541,
7542,
7543,
7544,
7550,
7551,
7552,
7553,
7554,
7555,
7600,
7610,
7611,
7620,
7621,
7622,
7630,
7631,
7632,
7633,
7640,
7641,
7642,
7643,
7644,
7650,
7651,
7652,
7653,
7654,
7655,
7660,
7661,
7662,
7663,
7664,
7665,
7666,
7700,
7710,
7711,
7720,
7721,
7722,
7730,
7731,
7732,
7733,
7740,
7741,
7742,
7743,
7744,
7750,
7751,
7752,
7753,
7754,
7755,
7760,
7761,
7762,
7763.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 3268744 values, from 1 to 999999999999999).
n\r | 0 | 1 |
2 | 2322951 | 945793 | 2 |
3 | 1089748 | 1089498 | 1089498 | 3 |
4 | 1494119 | 322831 | 828832 | 622962 | 4 |
5 | 1972869 | 820250 | 320450 | 116400 | 38775 | 5 |
6 | 774432 | 315251 | 774272 | 315316 | 774247 | 315226 | 6 |
7 | 466977 | 466962 | 466964 | 466964 | 466961 | 466952 | 466964 | 7 |
8 | 907538 | 107713 | 292639 | 233683 | 586581 | 215118 | 536193 | 389279 | 8 |
9 | 363254 | 363166 | 363166 | 363247 | 363166 | 363166 | 363247 | 363166 | 363166 | 9 |
10 | 1961241 | 817190 | 319770 | 116280 | 38760 | 11628 | 3060 | 680 | 120 | 15 | 10 |
11 | 38880 | 83512 | 202631 | 355784 | 494351 | 566280 | 544753 | 442156 | 300729 | 167596 | 72072 |
A pictorial representation of the table above
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.