The oban numbers up to 1015 :
3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 50, 53, 55, 56, 57, 58, 59, 60, 63, 65, 66, 67, 68, 69, 70, 73, 75, 76, 77, 78, 79, 80, 83, 85, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98, 99, 300, 303, 305, 306, 307, 308, 309, 310, 311, 312, 313, 315, 316, 317, 318, 319, 320, 323, 325, 326, 327, 328, 329, 330, 333, 335, 336, 337, 338, 339, 350, 353, 355, 356, 357, 358, 359, 360, 363, 365, 366, 367, 368, 369, 370, 373, 375, 376, 377, 378, 379, 380, 383, 385, 386, 387, 388, 389, 390, 393, 395, 396, 397, 398, 399, 500, 503, 505, 506, 507, 508, 509, 510, 511, 512, 513, 515, 516, 517, 518, 519, 520, 523, 525, 526, 527, 528, 529, 530, 533, 535, 536, 537, 538, 539, 550, 553, 555, 556, 557, 558, 559, 560, 563, 565, 566, 567, 568, 569, 570, 573, 575, 576, 577, 578, 579, 580, 583, 585, 586, 587, 588, 589, 590, 593, 595, 596, 597, 598, 599, 600, 603, 605, 606, 607, 608, 609, 610, 611, 612, 613, 615, 616, 617, 618, 619, 620, 623, 625, 626, 627, 628, 629, 630, 633, 635, 636, 637, 638, 639, 650, 653, 655, 656, 657, 658, 659, 660, 663, 665, 666, 667, 668, 669, 670, 673, 675, 676, 677, 678, 679, 680, 683, 685, 686, 687, 688, 689, 690, 693, 695, 696, 697, 698, 699, 700, 703, 705, 706, 707, 708, 709, 710, 711, 712, 713, 715, 716, 717, 718, 719, 720, 723, 725, 726, 727, 728, 729, 730, 733, 735, 736, 737, 738, 739, 750, 753, 755, 756, 757, 758, 759, 760, 763, 765, 766, 767, 768, 769, 770, 773, 775, 776, 777, 778, 779, 780, 783, 785, 786, 787, 788, 789, 790, 793, 795, 796, 797, 798, 799, 800, 803, 805, 806, 807, 808, 809, 810, 811, 812, 813, 815, 816, 817, 818, 819, 820, 823, 825, 826, 827, 828, 829, 830, 833, 835, 836, 837, 838, 839, 850, 853, 855, 856, 857, 858, 859, 860, 863, 865, 866, 867, 868, 869, 870, 873, 875, 876, 877, 878, 879, 880, 883, 885, 886, 887, 888, 889, 890, 893, 895, 896, 897, 898, 899, 900, 903, 905, 906, 907, 908, 909, 910, 911, 912, 913, 915, 916, 917, 918, 919, 920, 923, 925, 926, 927, 928, 929, 930, 933, 935, 936, 937, 938, 939, 950, 953, 955, 956, 957, 958, 959, 960, 963, 965, 966, 967, 968, 969, 970, 973, 975, 976, 977, 978, 979, 980, 983, 985, 986, 987, 988, 989, 990, 993, 995, 996, 997, 998, 999.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 454 values, from 3 to 999).
| n\r | 0 | 1 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 195 | 259 | 2 | ||||||||
| 3 | 154 | 142 | 158 | 3 | |||||||
| 4 | 97 | 126 | 98 | 133 | 4 | ||||||
| 5 | 125 | 70 | 70 | 126 | 63 | 5 | |||||
| 6 | 67 | 83 | 69 | 87 | 59 | 89 | 6 | ||||
| 7 | 63 | 65 | 66 | 64 | 65 | 65 | 66 | 7 | |||
| 8 | 48 | 63 | 48 | 66 | 49 | 63 | 50 | 67 | 8 | ||
| 9 | 49 | 47 | 51 | 52 | 47 | 54 | 53 | 48 | 53 | 9 | |
| 10 | 62 | 7 | 7 | 63 | 0 | 63 | 63 | 63 | 63 | 63 | 10 |
| 11 | 42 | 40 | 39 | 43 | 39 | 42 | 43 | 41 | 43 | 43 | 39 |
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.
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