Generalization regarding base-b proper fractions n/d having nontrivial anomalous cancellation 
with 2 <= b <= 120 and d <= b^2 + b.
Michael De Vlieger, St. Louis, Missouri 201709132030, updated 201709150800.

A trivial anomalous cancellation involves digit k = 0 for numerator n and denominator d
both such that they are congruent to 0 (mod b).

In this document, the word "qualified" means that the term is in A292288 or A292289, 
that is, the number in question pertains to a base-b proper fraction with nontrivial 
anomalous cancellation.

There are several parts to this document:
1. General analysis
2. Record transform and indices for i = number of qualified denominators d < b^2
3. Irregular triangle: list of qualified denominators <= b^2 + b
4. Irregular triangle: list of numerators pertaining to qualified denominators
5. Algorithm

//////////// 1.

General analysis.

b = base and index
n = A292288(b) = smallest numerator that pertains to d
d = A292289(b) = smallest qualified denominator
n/d = simplified ratio of numerator n and denominator d
i = number of qualified denominators d < b^2
k = base-b digit cancelled in the numerator and denominator to arrive at n/d
b-n+1 = difference between base and numerator plus one.
b^2-d = difference between the square of the base and denominator.
N = numerator pertaining to D
D = largest qualified denominator D < b^2, or "-" if none.
N/D = simplified ratio of numerator N and denominator D
b^2-D = difference between b^2 and D

  b     n       d   n/d      i     k   b-n+1   b^2-d    N       D   N/D b^2-D   b
---------------------------------------------------------------------------------
  2     3       6   1/2      0     1     0      -2      -       -     -   -     2
  3     4      12   1/3      0     1     0      -3      -       -     -   -     3
  4     7      14   1/2      1     3     2       2      7      14   1/2   2     4
  5     6      30   1/5      0     1     0      -5      -       -     -   -     5
  6    11      33   1/3      2     5     4       3     17      34   1/2   2     6
  7     8      56   1/7      0     1     0      -7      -       -     -   -     7
  8    15      60   1/4      2     7     6       4     31      62   1/2   2     8
  9    13      39   1/3      2     4     3      42     26      78   1/3   3     9
 10    16      64   1/4      4     6     5      36     49      98   1/2   2    10
 11    12     132   1/11     0     1     0     -11      -       -     -   -    11
 12    23     138   1/6      4    11    10       6     71     142   1/2   2    12
 13    14     182   1/13     0     1     0     -13      -       -     -   -    13
 14    27     189   1/7      2    13    12       7     97     194   1/2   2    14
 15    22     110   1/5      6     7     6     115     74     222   1/3   3    15
 16    21      84   1/4      7     5     4     172    127     254   1/2   2    16
 17    18     306   1/17     0     1     0     -17      -       -     -   -    17
 18    35     315   1/9      4    17    16       9    161     322   1/2   2    18
 19    20     380   1/19     0     1     0     -19      -       -     -   -    19
 20    39     390   1/10     4    19    18      10    199     398   1/2   2    20
 21    29     174   1/6     10     8     7     267    146     438   1/3   3    21
 22    34     272   1/8      6    12    11     212    241     482   1/2   2    22
 23    24     552   1/23     0     1     0     -23      -       -     -   -    23
 24    47     564   1/12     6    23    22      12    287     574   1/2   2    24
 25    31     155   1/5      6     6     5     470    124     620   1/5   5    25
 26    67     402   1/6      4    15    40     274    337     674   1/2   2    26
 27    40     360   1/9      6    13    12     369    242     726   1/3   3    27
 28    37     259   1/7     10     9     8     525    391     782   1/2   2    28
 29    30     870   1/29     0     1     0     -29      -       -     -   -    29
 30    59     885   1/15     6    29    28      15    449     898   1/2   2    30
 31    32     992   1/31     0     1     0     -31      -       -     -   -    31
 32    63    1008   1/16     4    31    30      16    511    1022   1/2   2    32
 33    45     405   1/9      8    12    11     684    362    1086   1/3   3    33
 34    52     624   1/12     6    18    17     532    577    1154   1/2   2    34
 35    87     609   1/7      6    17    51     616    244    1220   1/5   5    35
 36    43     258   1/6     21     7     6    1038    647    1294   1/2   2    36
 37    38    1406   1/37     0     1     0     -37      -       -     -   -    37
 38    75    1425   1/19     2    37    36      19    721    1442   1/2   2    38
 39    58     754   1/13     6    19    18     767    506    1518   1/3   3    39
 40    53     530   1/10    18    13    12    1070    799    1598   1/2   2    40
 41    42    1722   1/41     0     1     0     -41      -       -     -   -    41
 42    83    1743   1/21     6    41    40      21    881    1762   1/2   2    42
 43    44    1892   1/43     0     1     0     -43      -       -     -   -    43
 44    87    1914   1/22     4    43    42      22    967    1934   1/2   2    44
 45    56     504   1/9     18    11    10    1521    674    2022   1/3   3    45
 46    70    1120   1/16    10    24    23     996   1057    2114   1/2   2    46
 47    48    2256   1/47     0     1     0     -47      -       -     -   -    47
 48    95    2280   1/24     8    47    46      24   1151    2302   1/2   2    48
 49    57     399   1/7     10     8     7    2002    342    2394   1/7   7    49
 50    71    1065   1/15    10    21    20    1435   1249    2498   1/2   2    50
 51   122    1037   2/17    12    20    70    1564    866    2598   1/3   3    51
 52    69     897   1/13    12    17    16    1807   1351    2702   1/2   2    52
 53    54    2862   1/53     0     1     0     -53      -       -     -   -    53
 54   107    2889   1/27     6    53    52      27   1457    2914   1/2   2    54
 55    67     670   1/10    16    12    11    2355    604    3020   1/5   5    55
 56    71     852   1/12    22    15    14    2284   1567    3134   1/2   2    56
 57    77    1155   1/15    14    20    19    2094   1082    3246   1/3   3    57
 58    88    1760   1/20     6    30    29    1604   1681    3362   1/2   2    58
 59    60    3540   1/59     0     1     0     -59      -       -     -   -    59
 60   119    3570   1/30    10    59    58      30   1799    3598   1/2   2    60
 61    62    3782   1/61     0     1     0     -61      -       -     -   -    61
 62   123    3813   1/31     2    61    60      31   1921    3842   1/2   2    62
 63    94    1974   1/21    12    31    30    1995   1322    3966   1/3   3    63
 64    73     584   1/8     21     9     8    3512   2047    4094   1/2   2    64
 65    81    1053   1/13    12    16    15    3172    844    4220   1/5   5    65
 66    79     869   1/11    20    13    12    3487   2177    4354   1/2   2    66
 67    68    4556   1/67     0     1     0     -67      -       -     -   -    67
 68   135    4590   1/34     4    67    66      34   2311    4622   1/2   2    68
 69    93    1674   1/18    10    24    23    3087   1586    4758   1/3   3    69
 70   163    1630   1/10    22    23    92    3270   2449    4898   1/2   2    70
 71    72    5112   1/71     0     1     0     -71      -       -     -   -    71
 72   143    5148   1/36    10    71    70      36   2591    5182   1/2   2    72
 73    74    5402   1/73     0     1     0     -73      -       -     -   -    73
 74   147    5439   1/37     2    73    72      37   2737    5474   1/2   2    74
 75   112    2800   1/25    12    37    36    2825   1874    5622   1/3   3    75
 76    96    1536   1/16    20    20    19    4240   2887    5774   1/2   2    76
 77   178    1869   2/21    14    24   100    4060    846    5922   1/7   7    77
 78    92    1104   1/12    24    14    13    4980   3041    6082   1/2   2    78
 79    80    6320   1/79     0     1     0     -79      -       -     -   -    79
 80   159    6360   1/40     8    79    78      40   3199    6398   1/2   2    80
 81    91     819   1/9     24    10     9    5742   2186    6558   1/3   3    81
 82   124    3472   1/28     8    42    41    3252   3361    6722   1/2   2    82
 83    84    6972   1/83     0     1     0     -83      -       -     -   -    83
 84   167    7014   1/42    10    83    82      42   3527    7054   1/2   2    84
 85   103    1545   1/15    28    18    17    5680   1444    7220   1/5   5    85
 86   217    3906   1/18     6    45   130    3490   3697    7394   1/2   2    86
 87   130    3770   1/29     6    43    42    3799   2522    7566   1/3   3    87
 88   117    2574   1/22    18    29    28    5170   3871    7742   1/2   2    88
 89    90    8010   1/89     0     1     0     -89      -       -     -   -    89
 90   179    8055   1/45    10    89    88      45   4049    8098   1/2   2    90
 91   106    1378   1/13    28    15    14    6903   1182    8274   1/7   7    91
 92   210    2415   2/23    16    26   117    6049   4231    8462   1/2   2    92
 93   125    3000   1/24    10    32    31    5649   2882    8646   1/3   3    93
 94   142    4544   1/32     6    48    47    4292   4417    8834   1/2   2    94
 95   237    4503   1/19     6    47   141    4522   1804    9020   1/5   5    95
 96   115    1840   1/16    30    19    18    7376   4607    9214   1/2   2    96
 97    98    9506   1/97     0     1     0     -97      -       -     -   -    97
 98   195    9555   1/49     4    97    96      49   4801    9602   1/2   2    98
 99   127    2794   1/22    24    28    27    7007   3266    9798   1/3   3    99
100   111    1110   1/10    37    11    10    8890   4999    9998   1/2   2   100
101   102   10302   1/101    0     1     0    -101      -       -     -   -   101
102   203   10353   1/51     6   101   100      51   5201   10402   1/2   2   102
103   104   10712   1/103    0     1     0    -103      -       -     -   -   103
104   207   10764   1/52     6   103   102      52   5407   10814   1/2   2   104
105   121    1694   1/14    46    16    15    9331   3674   11022   1/3   3   105
106   160    5760   1/36    14    54    53    5476   5617   11234   1/2   2   106
107   108   11556   1/107    0     1     0    -107      -       -     -   -   107
108   215   11610   1/54    10   107   106      54   5831   11662   1/2   2   108
109   110   11990   1/109    0     1     0    -109      -       -     -   -   109
110   219   12045   1/55     6   109   108      55   6049   12098   1/2   2   110
111   373    4476   1/12    18    40   261    7845   4106   12318   1/3   3   111
112   149    4172   1/28    24    37    36    8372   6271   12542   1/2   2   112
113   114   12882   1/113    0     1     0    -113      -       -     -   -   113
114   227   12939   1/57     6   113   112      57   6497   12994   1/2   2   114
115   139    2780   1/20    18    24    23   10445   2644   13220   1/5   5   115
116   146    3504   1/24    14    30    29    9952   6727   13454   1/2   2   116
117   263    3419   1/13    20    29   145   10270   4562   13686   1/3   3   117
118   178    7120   1/40    10    60    59    6804   6961   13922   1/2   2   118
119   416    7072   1/17     6    59   296    7089   2022   14154   1/7   7   119
120   137    2055   1/15    50    17    16   12345   7199   14398   1/2   2   120

Observations:
1. For prime base p, (p + 1)/(p^2 + p) simplifies to 1/p by cancelling digit k = 1 
   in the numerator and denominator.
2. Smallest base b for which n/d, simplified, has a numerator greater than 1 is 51.
   The next terms are 77 and 92.
3. Let q = the least prime divisor of composite b. The fraction with the largest 
   qualified denominator, N/D, simplifies to 1/q, and the denominator D = b - q.

///////////// 2.

Record transform for i = number of qualified denominators d < b^2.

index i     b
-------------
 1    0     2
 2    1     4
 3    2     6
 4    4    10
 5    6    15
 6    7    16
 7   10    21
 8   21    36
 9   22    56
10   24    78
11   28    85
12   30    96
13   37   100
14   46   105
15   50   120

///////////// 3.

Irregular number triangle: list of qualified denominators less than or equal to b^2 + b
for 2 <= b <= 120:

2: {6}
3: {12}
4: {14, 20}
5: {30}
6: {33, 34, 42}
7: {56}
8: {60, 62, 72}
9: {39, 78, 90}
10: {64, 65, 95, 98, 110}
11: {132}
12: {138, 140, 141, 142, 156}
13: {182}
14: {189, 194, 210}
15: {110, 111, 189, 190, 220, 222, 240}
16: {84, 150, 152, 168, 248, 252, 254, 272}
17: {306}
18: {315, 318, 321, 322, 342}
19: {380}
20: {390, 395, 396, 398, 420}
21: {174, 175, 217, 219, 324, 329, 348, 350, 434, 438, 462}
22: {272, 275, 319, 320, 473, 482, 506}
23: {552}
24: {564, 568, 570, 572, 573, 574, 600}
25: {155, 310, 410, 415, 465, 620, 650}
26: {402, 403, 663, 674, 702}
27: {360, 363, 555, 558, 720, 726, 756}
28: {259, 260, 430, 434, 518, 520, 770, 777, 780, 782, 812}
29: {870}
30: {885, 890, 894, 895, 897, 898, 930}
31: {992}
32: {1008, 1016, 1020, 1022, 1056}
33: {405, 407, 539, 543, 810, 814, 1078, 1086, 1122}
34: {624, 629, 765, 768, 1139, 1154, 1190}
35: {609, 610, 860, 861, 1218, 1220, 1260}
36: {258, 368, 369, 516, 736, 738, 774, 915, 924, 1024, 1032, 1035, 1104, 1107, 1278, 1284, 1287, 1290, 1292, 1293, 1294, 1332}
37: {1406}
38: {1425, 1442, 1482}
39: {754, 759, 1113, 1118, 1508, 1518, 1560}
40: {530, 532, 735, 736, 854, 860, 1056, 1060, 1064, 1065, 1470, 1472, 1580, 1590, 1592, 1595, 1596, 1598, 1640}
41: {1722}
42: {1743, 1750, 1757, 1758, 1761, 1762, 1806}
43: {1892}
44: {1914, 1925, 1932, 1934, 1980}
45: {504, 505, 732, 735, 1005, 1008, 1010, 1011, 1375, 1377, 1464, 1470, 1512, 1515, 2010, 2016, 2020, 2022, 2070}
46: {1120, 1127, 1170, 1173, 1265, 1266, 1403, 1408, 2093, 2114, 2162}
47: {2256}
48: {2280, 2288, 2292, 2296, 2298, 2300, 2301, 2302, 2352}
49: {399, 798, 1197, 1596, 1785, 1799, 1995, 2240, 2247, 2394, 2450}
50: {1065, 1070, 1424, 1425, 2130, 2140, 2475, 2490, 2495, 2498, 2550}
51: {1037, 1038, 1292, 1299, 1806, 1819, 1863, 1870, 2074, 2076, 2584, 2598, 2652}
52: {897, 900, 1422, 1430, 1794, 1800, 2379, 2380, 2678, 2691, 2700, 2702, 2756}
53: {2862}
54: {2889, 2898, 2907, 2910, 2913, 2914, 2970}
55: {670, 671, 1340, 1342, 1507, 1510, 2002, 2010, 2013, 2015, 2500, 2519, 2680, 2684, 3014, 3020, 3080}
56: {852, 854, 1248, 1253, 1704, 1708, 1869, 1876, 1878, 1880, 2496, 2506, 2556, 2562, 2835, 2848, 3108, 3122, 3128, 3129, 3132, 3134, 3192}
57: {1155, 1159, 1215, 1216, 1615, 1623, 2310, 2318, 2430, 2432, 2774, 2781, 3230, 3246, 3306}
58: {1760, 1769, 2233, 2240, 3335, 3362, 3422}
59: {3540}
60: {3570, 3580, 3585, 3588, 3590, 3594, 3595, 3596, 3597, 3598, 3660}
61: {3782}
62: {3813, 3842, 3906}
63: {1974, 1980, 1981, 1983, 2555, 2556, 2805, 2814, 3948, 3960, 3962, 3966, 4032}
64: {584, 1168, 1360, 1364, 1752, 2134, 2144, 2270, 2272, 2336, 2720, 2728, 2920, 3164, 3184, 3504, 4064, 4080, 4088, 4092, 4094, 4160}
65: {1053, 1055, 2106, 2110, 2625, 2639, 2765, 2769, 3159, 3165, 4212, 4220, 4290}
66: {869, 870, 1738, 1740, 2338, 2343, 2607, 2610, 2997, 3014, 3344, 3345, 3476, 3480, 4323, 4334, 4345, 4350, 4353, 4354, 4422}
67: {4556}
68: {4590, 4607, 4620, 4622, 4692}
69: {1674, 1679, 2369, 2379, 3348, 3358, 3564, 3565, 4738, 4758, 4830}
70: {1630, 1631, 2125, 2128, 2544, 2555, 3248, 3255, 3260, 3262, 3264, 3265, 4250, 4256, 4459, 4470, 4865, 4886, 4890, 4893, 4895, 4898, 4970}
71: {5112}
72: {5148, 5160, 5166, 5172, 5175, 5176, 5178, 5180, 5181, 5182, 5256}
73: {5402}
74: {5439, 5474, 5550}
75: {2800, 2805, 2810, 2811, 3640, 3645, 3939, 3950, 5600, 5610, 5620, 5622, 5700}
76: {1536, 1539, 1919, 1924, 2990, 3002, 3072, 3078, 3458, 3462, 3838, 3848, 4608, 4617, 4844, 4845, 5738, 5757, 5772, 5774, 5852}
77: {1869, 1870, 2959, 2961, 3738, 3740, 4422, 4431, 4444, 4445, 5607, 5610, 5918, 5922, 6006}
78: {1104, 1105, 2208, 2210, 3312, 3315, 3471, 3472, 4335, 4342, 4416, 4420, 5184, 5200, 5211, 5213, 5520, 5525, 6045, 6058, 6071, 6078, 6081, 6082, 6162}
79: {6320}
80: {6360, 6380, 6384, 6390, 6392, 6395, 6396, 6398, 6480}
81: {819, 1638, 2289, 2295, 2457, 2619, 2622, 3267, 3276, 3279, 4095, 4488, 4509, 4578, 4590, 4914, 5220, 5238, 5244, 5247, 5733, 6534, 6552, 6558, 6642}
82: {3472, 3485, 3730, 3731, 4469, 4480, 6683, 6722, 6806}
83: {6972}
84: {7014, 7028, 7035, 7042, 7044, 7049, 7050, 7052, 7053, 7054, 7140}
85: {1545, 1547, 1802, 1805, 3000, 3009, 3090, 3094, 3604, 3610, 4635, 4641, 4794, 4810, 4811, 4815, 5406, 5415, 6000, 6018, 6171, 6180, 6188, 6190, 6868, 6875, 7208, 7220, 7310}
86: {3906, 3913, 4429, 4434, 7353, 7394, 7482}
87: {3770, 3783, 5265, 5278, 7540, 7566, 7656}
88: {2574, 2580, 3200, 3201, 3990, 4004, 5148, 5152, 5159, 5160, 6400, 6402, 7700, 7722, 7733, 7736, 7740, 7742, 7832}
89: {8010}
90: {8055, 8070, 8082, 8085, 8090, 8091, 8094, 8095, 8097, 8098, 8190}
91: {1378, 1379, 2478, 2483, 2756, 2758, 3302, 3311, 3668, 3679, 4134, 4137, 4956, 4966, 5145, 5148, 5512, 5516, 6604, 6622, 6890, 6895, 7336, 7358, 7434, 7449, 8268, 8274, 8372}
92: {2415, 2416, 4550, 4554, 4830, 4832, 6480, 6509, 7245, 7248, 7797, 7808, 8418, 8441, 8460, 8462, 8556}
93: {3000, 3007, 4309, 4323, 6000, 6014, 6479, 6480, 8618, 8646, 8742}
94: {4544, 4559, 5875, 5888, 8789, 8834, 8930}
95: {4503, 4510, 5750, 5757, 9006, 9020, 9120}
96: {1840, 1842, 2420, 2424, 3680, 3684, 4840, 4848, 5508, 5520, 5526, 5528, 6279, 6304, 6783, 6784, 7260, 7272, 7360, 7368, 9168, 9184, 9192, 9200, 9204, 9208, 9210, 9212, 9213, 9214, 9312}
97: {9506}
98: {9555, 9590, 9597, 9602, 9702}
99: {2794, 2799, 3495, 3498, 4884, 4895, 4896, 4899, 5580, 5588, 5598, 5599, 5994, 5995, 6783, 6798, 6990, 6996, 8382, 8397, 9768, 9790, 9792, 9798, 9900}
100: {1110, 2220, 2724, 2725, 3325, 3330, 3332, 4235, 4240, 4440, 5134, 5150, 5448, 5450, 5550, 6640, 6650, 6660, 6664, 6665, 7756, 7770, 7775, 8145, 8172, 8175, 8180, 8470, 8480, 8880, 9950, 9975, 9980, 9990, 9995, 9996, 9998, 10100}
101: {10302}
102: {10353, 10370, 10387, 10398, 10401, 10402, 10506}
103: {10712}
104: {10764, 10790, 10803, 10808, 10812, 10814, 10920}
105: {1694, 1695, 2751, 2755, 3388, 3390, 3807, 3815, 4130, 4131, 5082, 5085, 5495, 5502, 5505, 5509, 5510, 5511, 6760, 6776, 6780, 6783, 6875, 6888, 6985, 6993, 7614, 7630, 8235, 8253, 8260, 8262, 8265, 8267, 8470, 8475, 9604, 9645, 10164, 10170, 10990, 11004, 11010, 11018, 11020, 11022, 11130}
106: {5760, 5777, 5874, 5883, 5984, 5989, 6413, 6416, 6731, 6738, 7473, 7488, 11183, 11234, 11342}
107: {11556}
108: {11610, 11628, 11637, 11646, 11652, 11655, 11658, 11660, 11661, 11662, 11772}
109: {11990}
110: {12045, 12078, 12089, 12090, 12095, 12098, 12210}
111: {4476, 4477, 4921, 4926, 6142, 6159, 8370, 8399, 8493, 8510, 8610, 8621, 8952, 8954, 9842, 9852, 12284, 12318, 12432}
112: {4172, 4176, 4179, 4180, 5080, 5082, 6422, 6440, 8344, 8352, 8358, 8360, 10160, 10164, 11165, 11184, 12488, 12516, 12528, 12530, 12536, 12537, 12540, 12542, 12656}
113: {12882}
114: {12939, 12958, 12977, 12990, 12993, 12994, 13110}
115: {2780, 2783, 5560, 5566, 6601, 6610, 8340, 8349, 8786, 8809, 8810, 8815, 11000, 11017, 11120, 11132, 13202, 13220, 13340}
116: {3504, 3509, 7008, 7018, 8062, 8070, 10512, 10527, 10752, 10759, 13398, 13427, 13452, 13454, 13572}
117: {3419, 3420, 4710, 4719, 6825, 6838, 6840, 6843, 8253, 8255, 9420, 9438, 10257, 10260, 13195, 13212, 13650, 13676, 13680, 13686, 13806}
118: {7120, 7139, 7490, 7493, 7729, 7730, 9263, 9280, 13865, 13922, 14042}
119: {7072, 7077, 8631, 8636, 14144, 14154, 14280}
120: {2055, 2056, 2538, 2540, 4110, 4112, 5076, 5080, 5915, 5928, 6156, 6165, 6168, 6170, 7614, 7620, 8220, 8224, 10152, 10160, 10250, 10275, 10280, 10284, 10972, 11010, 11830, 11856, 12312, 12320, 12330, 12336, 12339, 12340, 12690, 12700, 14340, 14360, 14370, 14376, 14380, 14385, 14388, 14390, 14392, 14394, 14395, 14396, 14397, 14398, 14520}

//////////// 4.

Irregular number triangle: list of numerators pertaining to qualified denominators less than 
or equal to b^2 + b for 2 <= b <= 120:

2: {3}
3: {4}
4: {7, 5}
5: {6}
6: {11, 17, 7}
7: {8}
8: {15, 31, 9}
9: {13, 26, 10}
10: {16, 26, 19, 49, 11}
11: {12}
12: {23, 35, 47, 71, 13}
13: {14}
14: {27, 97, 15}
15: {22, 37, 42, 57, 44, 74, 16}
16: {21, 25, 57, 42, 31, 63, 127, 17}
17: {18}
18: {35, 53, 107, 161, 19}
19: {20}
20: {39, 79, 99, 199, 21}
21: {29, 50, 31, 73, 36, 141, 58, 100, 62, 146, 22}
22: {34, 100, 58, 80, 43, 241, 23}
23: {24}
24: {47, 71, 95, 143, 191, 287, 25}
25: {31, 62, 41, 166, 93, 124, 26}
26: {67, 93, 51, 337, 27}
27: {40, 121, 74, 155, 80, 242, 28}
28: {37, 65, 43, 155, 74, 130, 55, 111, 195, 391, 29}
29: {30}
30: {59, 89, 149, 179, 299, 449, 31}
31: {32}
32: {63, 127, 255, 511, 33}
33: {45, 111, 49, 181, 90, 222, 98, 362, 34}
34: {52, 222, 90, 192, 67, 577, 35}
35: {87, 122, 129, 164, 174, 244, 36}
36: {43, 46, 82, 86, 92, 164, 129, 61, 385, 64, 172, 460, 138, 246, 71, 107, 143, 215, 323, 431, 647, 37}
37: {38}
38: {75, 721, 39}
39: {58, 253, 106, 301, 116, 506, 40}
40: {53, 133, 98, 138, 61, 301, 66, 106, 266, 426, 196, 276, 79, 159, 199, 319, 399, 799, 41}
41: {42}
42: {83, 125, 251, 293, 587, 881, 43}
43: {44}
44: {87, 175, 483, 967, 45}
45: {56, 101, 61, 196, 67, 112, 202, 337, 165, 255, 122, 392, 168, 303, 134, 224, 404, 674, 46}
46: {70, 392, 117, 255, 165, 211, 122, 352, 91, 1057, 47}
47: {48}
48: {95, 143, 191, 287, 383, 575, 767, 1151, 49}
49: {57, 114, 171, 228, 85, 771, 285, 192, 535, 342, 50}
50: {71, 321, 178, 228, 142, 642, 99, 249, 499, 1249, 51}
51: {122, 173, 76, 433, 86, 749, 138, 495, 244, 346, 152, 866, 52}
52: {69, 225, 79, 495, 138, 450, 305, 357, 103, 207, 675, 1351, 53}
53: {54}
54: {107, 161, 323, 485, 971, 1457, 55}
55: {67, 122, 134, 244, 137, 302, 91, 201, 366, 806, 100, 1145, 268, 488, 274, 604, 56}
56: {71, 183, 78, 358, 142, 366, 89, 201, 313, 705, 156, 716, 213, 549, 162, 890, 111, 223, 391, 447, 783, 1567, 57}
57: {77, 305, 135, 192, 85, 541, 154, 610, 270, 384, 219, 618, 170, 1082, 58}
58: {88, 610, 154, 560, 115, 1681, 59}
59: {60}
60: {119, 179, 239, 299, 359, 599, 719, 899, 1199, 1799, 61}
61: {62}
62: {123, 1921, 63}
63: {94, 220, 283, 661, 292, 355, 170, 737, 188, 440, 566, 1322, 64}
64: {73, 146, 85, 341, 219, 97, 737, 227, 355, 292, 170, 682, 365, 113, 1393, 438, 127, 255, 511, 1023, 2047, 65}
65: {81, 211, 162, 422, 105, 1015, 237, 497, 243, 633, 324, 844, 66}
66: {79, 145, 158, 290, 167, 497, 237, 435, 111, 1233, 380, 446, 316, 580, 131, 197, 395, 725, 1451, 2177, 67}
67: {68}
68: {135, 271, 1155, 2311, 69}
69: {93, 438, 103, 793, 186, 876, 396, 465, 206, 1586, 70}
70: {163, 233, 170, 380, 106, 876, 116, 186, 326, 466, 816, 1306, 340, 760, 273, 1043, 139, 349, 489, 699, 979, 2449, 71}
71: {72}
72: {143, 215, 287, 431, 575, 647, 863, 1295, 1727, 2591, 73}
73: {74}
74: {147, 2737, 75}
75: {112, 187, 562, 937, 273, 648, 202, 1027, 224, 374, 1124, 1874, 76}
76: {96, 324, 101, 481, 115, 1027, 192, 648, 273, 577, 202, 962, 288, 972, 519, 595, 151, 303, 1443, 2887, 77}
77: {178, 255, 269, 423, 356, 510, 134, 211, 1212, 1905, 534, 765, 538, 846, 78}
78: {92, 170, 184, 340, 276, 510, 356, 434, 289, 835, 368, 680, 144, 300, 1158, 2406, 460, 850, 155, 233, 467, 1013, 2027, 3041, 79}
79: {80}
80: {159, 319, 399, 639, 799, 1279, 1599, 3199, 81}
81: {91, 182, 109, 595, 273, 194, 437, 121, 364, 1093, 455, 136, 1837, 218, 1190, 546, 145, 388, 874, 2332, 637, 242, 728, 2186, 82}
82: {124, 1190, 373, 455, 218, 1120, 163, 3361, 83}
83: {84}
84: {167, 251, 335, 503, 587, 1007, 1175, 1763, 2351, 3527, 85}
85: {103, 273, 106, 361, 120, 885, 206, 546, 212, 722, 309, 819, 141, 481, 566, 1926, 318, 1083, 240, 1770, 242, 412, 1092, 1857, 505, 1100, 424, 1444, 86}
86: {217, 819, 309, 739, 171, 3697, 87}
87: {130, 1261, 234, 1365, 260, 2522, 88}
88: {117, 645, 300, 388, 133, 1365, 234, 322, 938, 1290, 600, 776, 175, 351, 703, 967, 1935, 3871, 89}
89: {90}
90: {179, 269, 449, 539, 809, 899, 1349, 1619, 2699, 4049, 91}
91: {106, 197, 118, 573, 212, 394, 127, 946, 131, 1132, 318, 591, 236, 1146, 420, 693, 424, 788, 254, 1892, 530, 985, 262, 2264, 354, 1719, 636, 1182, 92}
92: {210, 302, 325, 693, 420, 604, 162, 2830, 630, 906, 452, 1464, 183, 367, 2115, 4231, 93}
93: {125, 776, 139, 1441, 250, 1552, 627, 720, 278, 2882, 94}
94: {142, 1552, 250, 1472, 187, 4417, 95}
95: {237, 902, 345, 1010, 474, 1804, 96}
96: {115, 307, 121, 505, 230, 614, 242, 1010, 153, 345, 921, 2073, 161, 2561, 646, 742, 363, 1515, 460, 1228, 191, 287, 383, 575, 767, 1151, 1535, 2303, 3071, 4607, 97}
97: {98}
98: {195, 685, 1371, 4801, 99}
99: {127, 622, 233, 530, 148, 445, 544, 1633, 155, 254, 1244, 2036, 555, 654, 266, 1751, 466, 1060, 381, 1866, 296, 890, 1088, 3266, 100}
100: {111, 222, 227, 327, 133, 333, 833, 242, 742, 444, 151, 1751, 454, 654, 555, 166, 266, 666, 1666, 2666, 277, 777, 2177, 181, 681, 981, 3681, 484, 1484, 888, 199, 399, 499, 999, 1999, 2499, 4999, 101}
101: {102}
102: {203, 305, 611, 1733, 3467, 5201, 103}
103: {104}
104: {207, 415, 831, 1351, 2703, 5407, 105}
105: {121, 226, 131, 551, 242, 452, 141, 981, 354, 459, 363, 678, 157, 262, 367, 787, 1102, 1837, 169, 484, 904, 2584, 275, 1640, 381, 1221, 282, 1962, 183, 393, 708, 918, 1653, 3543, 605, 1130, 196, 4501, 726, 1356, 314, 524, 734, 1574, 2204, 3674, 106}
106: {160, 1962, 267, 1221, 374, 904, 484, 802, 381, 1123, 282, 1872, 211, 5617, 107}
107: {108}
108: {215, 323, 431, 647, 971, 1295, 1943, 2915, 3887, 5831, 109}
109: {110}
110: {219, 549, 1099, 1209, 2419, 6049, 111}
111: {373, 484, 266, 821, 166, 2053, 186, 3405, 298, 2185, 410, 1631, 746, 968, 532, 1642, 332, 4106, 112}
112: {149, 261, 597, 1045, 381, 605, 169, 2185, 298, 522, 1194, 2090, 762, 1210, 435, 2563, 223, 447, 783, 895, 1567, 1791, 3135, 6271, 113}
113: {114}
114: {227, 341, 683, 2165, 4331, 6497, 115}
115: {139, 484, 278, 968, 287, 1322, 417, 1452, 191, 766, 881, 3526, 440, 2395, 556, 1936, 574, 2644, 116}
116: {146, 726, 292, 1452, 417, 1345, 438, 2178, 672, 1484, 231, 463, 3363, 6727, 117}
117: {263, 380, 157, 1210, 175, 526, 760, 2281, 655, 889, 314, 2420, 789, 1140, 580, 2569, 350, 1052, 1520, 4562, 118}
118: {178, 2420, 535, 889, 655, 773, 314, 2320, 235, 6961, 119}
119: {416, 1011, 548, 1143, 832, 2022, 120}
120: {137, 257, 141, 381, 274, 514, 282, 762, 169, 1729, 171, 411, 771, 1851, 423, 1143, 548, 1028, 564, 1524, 205, 685, 1285, 4285, 211, 4771, 338, 3458, 342, 462, 822, 1542, 2742, 3702, 705, 1905, 239, 359, 479, 599, 719, 959, 1199, 1439, 1799, 2399, 2879, 3599, 4799, 7199, 121}

//////////// 5.

Algorithm:
This data was produced by Wolfram language 11.1 code that required about 8 hours in 
both of two sessions to generate. The first session generated n/d for 2 <= b <= 120.
Given the terms of the column "d" above and using that as a lower limit, the following
code supplies the essential data for this chart: (The first 30 terms can be generated in
minutes.)

With[{bb = 120, v = Import["b292289.txt", "Data"][[All, -1]]}, 
 Monitor[Table[
   Reap[Do[If[Length@ # > 0, Sow[#], #] &@
         Apply[Join, Map[{#, m} &, #]] &@
       Parallelize@
        Select[Range[b + 1, m - 1], 
         Function[k, 
          Function[{r, w, n, d}, 
               AnyTrue[
                Flatten@
                 Map[Apply[Outer[Divide, #1, #2] &, #] &, 
                  Transpose@
                   MapAt[# /. 0 -> Nothing &, 
                    Map[Function[x, 
                    Map[Map[FromDigits[#, b] &@ Delete[x, #] &, 
                    Position[x, #]] &, Intersection @@ {n, d}]], {n, 
                    d}], -1]], # == Divide @@ {k, m} &]] @@ {k/m, #, 
               First@ #, Last@ #} &@Map[IntegerDigits[#, b] &, {k, m}] -
            Boole[Mod[{k, m}, b] == {0, 0}]] ], {m, v[[b - 1]], 
       b^2 + b}]][[-1, -1]], {b, 2, bb}], 
  ProgressIndicator[b, {2, bb}]]]

(eof)