Base 3: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [2] [Base 3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192] [193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216] [217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240] [241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255]
[Odd Digit Sets]
[Even Digit Sets]
Final Numbers
[Fixed Points]
Cycles Lengths
[All Digit Sets]
[Odd Digit Sets]
[Even Digit Sets]
Iteration Frequencies
[Cycle Start]
[Full Cycle]
Maximum Iteration Sequences
[Cycle Start]
[Full Cycle]
Cycles Sequences
[Maximum Length Cycle Count]
[All Cycle Counts]

Radix Character Encoding
0	1	2

Color Key
Orange	Fixed Point	number that becomes itself after one iteration
Green	Final Numbers	all numbers eventually reached, from all cycles
Purple	Cycle Start	iterations include entry into cycle, assuming it repeats
Red	Full Cycle	iterations include entire cycle, proving it repeats
Blue	Start Numbers	subset (optimization) of all numbers; minimal for full coverage
Gray	No Results	any calculation that has no results

Digits	# Start Numbers	# Fixed Points (excluding zero)	# Cycles (including fixed) (excluding zero)	Full Cycle Max Length	Avg Steps including Cycle Start	Max Steps including Cycle Start	Avg Steps including Full Cycle	Max Steps including Full Cycle	# Final Numbers (excluding zero)
1	3	0 fixed pts	0 cycles	0 nodes	0.67 avg steps	1 max steps	1.67 avg steps	2 max steps	0 final numbers
2	6	0 fixed pts	0 cycles	0 nodes	1.67 avg steps	3 max steps	2.67 avg steps	4 max steps	0 final numbers
3	10	0 fixed pts	1 cycle	2 nodes	0.80 avg steps	1 max steps	2.50 avg steps	3 max steps	2 final numbers
4	15	0 fixed pts	1 cycle	2 nodes	1.40 avg steps	2 max steps	3.20 avg steps	4 max steps	2 final numbers
5	21	1 fixed pt	1 cycle	1 node	2.14 avg steps	4 max steps	3.14 avg steps	5 max steps	1 final number
6	28	0 fixed pts	1 cycle	3 nodes	1.64 avg steps	3 max steps	4.43 avg steps	6 max steps	3 final numbers
7	36	1 fixed pt	2 cycles	2 nodes	1.86 avg steps	4 max steps	3.58 avg steps	6 max steps	3 final numbers
8	45	1 fixed pt	1 cycle	1 node	2.80 avg steps	5 max steps	3.80 avg steps	6 max steps	1 final number
9	55	1 fixed pt	3 cycles	3 nodes	1.69 avg steps	4 max steps	4.13 avg steps	7 max steps	6 final numbers
10	66	1 fixed pt	2 cycles	4 nodes	2.09 avg steps	5 max steps	4.91 avg steps	7 max steps	5 final numbers
11	78	2 fixed pts	5 cycles	3 nodes	1.58 avg steps	4 max steps	3.97 avg steps	7 max steps	10 final numbers
12	91	1 fixed pt	2 cycles	2 nodes	2.87 avg steps	6 max steps	4.58 avg steps	8 max steps	3 final numbers
13	105	2 fixed pts	6 cycles	5 nodes	1.50 avg steps	4 max steps	5.08 avg steps	9 max steps	15 final numbers
14	120	2 fixed pts	3 cycles	2 nodes	3.17 avg steps	6 max steps	4.49 avg steps	8 max steps	4 final numbers
15	136	2 fixed pts	7 cycles	6 nodes	1.43 avg steps	4 max steps	5.76 avg steps	10 max steps	21 final numbers
16	153	2 fixed pts	4 cycles	3 nodes	2.58 avg steps	6 max steps	4.71 avg steps	8 max steps	7 final numbers
17	171	3 fixed pts	10 cycles	6 nodes	1.39 avg steps	4 max steps	4.96 avg steps	8 max steps	28 final numbers
18	190	2 fixed pts	5 cycles	5 nodes	2.37 avg steps	6 max steps	5.43 avg steps	8 max steps	12 final numbers
19	210	3 fixed pts	12 cycles	6 nodes	1.35 avg steps	4 max steps	5.13 avg steps	8 max steps	36 final numbers
20	231	3 fixed pts	6 cycles	3 nodes	2.83 avg steps	7 max steps	5.12 avg steps	10 max steps	11 final numbers
21	253	3 fixed pts	13 cycles	9 nodes	1.32 avg steps	4 max steps	6.76 avg steps	13 max steps	45 final numbers
22	276	3 fixed pts	7 cycles	3 nodes	2.96 avg steps	7 max steps	5.11 avg steps	10 max steps	13 final numbers
23	300	4 fixed pts	16 cycles	9 nodes	1.29 avg steps	4 max steps	6.02 avg steps	11 max steps	55 final numbers
24	325	3 fixed pts	8 cycles	5 nodes	2.61 avg steps	7 max steps	5.65 avg steps	10 max steps	18 final numbers
25	351	4 fixed pts	17 cycles	11 nodes	1.27 avg steps	4 max steps	7.74 avg steps	15 max steps	66 final numbers
26	378	4 fixed pts	9 cycles	5 nodes	3.17 avg steps	8 max steps	5.39 avg steps	10 max steps	19 final numbers
27	406	4 fixed pts	19 cycles	11 nodes	1.25 avg steps	4 max steps	7.75 avg steps	14 max steps	78 final numbers
28	435	4 fixed pts	10 cycles	6 nodes	2.59 avg steps	7 max steps	6.07 avg steps	11 max steps	25 final numbers
29	465	5 fixed pts	22 cycles	11 nodes	1.23 avg steps	4 max steps	7.63 avg steps	13 max steps	91 final numbers
30	496	4 fixed pts	11 cycles	6 nodes	2.69 avg steps	7 max steps	5.76 avg steps	11 max steps	28 final numbers
31	528	5 fixed pts	23 cycles	14 nodes	1.22 avg steps	4 max steps	9.27 avg steps	18 max steps	105 final numbers
32	561	5 fixed pts	14 cycles	6 nodes	2.46 avg steps	7 max steps	5.55 avg steps	11 max steps	35 final numbers
33	595	5 fixed pts	26 cycles	14 nodes	1.21 avg steps	4 max steps	7.96 avg steps	16 max steps	120 final numbers
34	630	5 fixed pts	15 cycles	6 nodes	2.50 avg steps	7 max steps	6.21 avg steps	11 max steps	41 final numbers
35	666	6 fixed pts	30 cycles	14 nodes	1.19 avg steps	4 max steps	7.72 avg steps	16 max steps	136 final numbers
36	703	5 fixed pts	16 cycles	6 nodes	2.72 avg steps	8 max steps	6.08 avg steps	12 max steps	43 final numbers
37	741	6 fixed pts	33 cycles	14 nodes	1.18 avg steps	4 max steps	8.45 avg steps	16 max steps	153 final numbers
38	780	6 fixed pts	18 cycles	6 nodes	2.78 avg steps	8 max steps	5.92 avg steps	12 max steps	47 final numbers
39	820	6 fixed pts	34 cycles	18 nodes	1.17 avg steps	4 max steps	10.25 avg steps	22 max steps	171 final numbers
40	861	6 fixed pts	19 cycles	9 nodes	2.59 avg steps	8 max steps	6.90 avg steps	13 max steps	56 final numbers
41	903	7 fixed pts	37 cycles	18 nodes	1.17 avg steps	4 max steps	9.57 avg steps	20 max steps	190 final numbers
42	946	6 fixed pts	20 cycles	9 nodes	2.88 avg steps	8 max steps	6.36 avg steps	13 max steps	58 final numbers
43	990	7 fixed pts	39 cycles	18 nodes	1.16 avg steps	4 max steps	9.72 avg steps	20 max steps	210 final numbers
44	1,035	7 fixed pts	23 cycles	9 nodes	2.56 avg steps	8 max steps	6.44 avg steps	13 max steps	68 final numbers
45	1,081	7 fixed pts	42 cycles	18 nodes	1.15 avg steps	4 max steps	9.34 avg steps	20 max steps	231 final numbers
46	1,128	7 fixed pts	24 cycles	9 nodes	2.62 avg steps	8 max steps	6.60 avg steps	13 max steps	73 final numbers
47	1,176	8 fixed pts	47 cycles	18 nodes	1.15 avg steps	4 max steps	9.42 avg steps	20 max steps	253 final numbers
48	1,225	7 fixed pts	25 cycles	11 nodes	2.47 avg steps	8 max steps	7.49 avg steps	15 max steps	84 final numbers
49	1,275	8 fixed pts	48 cycles	23 nodes	1.14 avg steps	4 max steps	11.66 avg steps	27 max steps	276 final numbers
50	1,326	8 fixed pts	26 cycles	11 nodes	2.99 avg steps	10 max steps	6.96 avg steps	15 max steps	85 final numbers
51	1,378	8 fixed pts	50 cycles	23 nodes	1.13 avg steps	4 max steps	11.98 avg steps	25 max steps	300 final numbers
52	1,431	8 fixed pts	28 cycles	11 nodes	2.54 avg steps	8 max steps	7.60 avg steps	16 max steps	97 final numbers
53	1,485	9 fixed pts	55 cycles	23 nodes	1.13 avg steps	4 max steps	10.80 avg steps	25 max steps	325 final numbers
54	1,540	8 fixed pts	29 cycles	11 nodes	2.58 avg steps	8 max steps	7.51 avg steps	16 max steps	103 final numbers
55	1,596	9 fixed pts	56 cycles	26 nodes	1.12 avg steps	4 max steps	13.24 avg steps	30 max steps	351 final numbers
56	1,653	9 fixed pts	32 cycles	11 nodes	2.46 avg steps	8 max steps	7.63 avg steps	16 max steps	116 final numbers
57	1,711	9 fixed pts	59 cycles	26 nodes	1.12 avg steps	4 max steps	12.86 avg steps	28 max steps	378 final numbers
58	1,770	9 fixed pts	33 cycles	11 nodes	2.66 avg steps	8 max steps	7.41 avg steps	16 max steps	119 final numbers
59	1,830	10 fixed pts	63 cycles	26 nodes	1.12 avg steps	4 max steps	12.19 avg steps	28 max steps	406 final numbers
60	1,891	9 fixed pts	34 cycles	14 nodes	2.46 avg steps	8 max steps	8.56 avg steps	19 max steps	133 final numbers
61	1,953	10 fixed pts	64 cycles	29 nodes	1.11 avg steps	4 max steps	14.55 avg steps	33 max steps	435 final numbers
62	2,016	10 fixed pts	37 cycles	14 nodes	2.49 avg steps	8 max steps	7.75 avg steps	19 max steps	140 final numbers
63	2,080	10 fixed pts	65 cycles	30 nodes	1.11 avg steps	4 max steps	15.62 avg steps	34 max steps	465 final numbers
64	2,145	10 fixed pts	40 cycles	14 nodes	2.40 avg steps	8 max steps	7.75 avg steps	19 max steps	155 final numbers
65	2,211	11 fixed pts	72 cycles	30 nodes	1.11 avg steps	4 max steps	13.65 avg steps	32 max steps	496 final numbers
66	2,278	10 fixed pts	41 cycles	14 nodes	2.52 avg steps	8 max steps	8.08 avg steps	19 max steps	162 final numbers
67	2,346	11 fixed pts	78 cycles	30 nodes	1.10 avg steps	4 max steps	13.28 avg steps	32 max steps	528 final numbers
68	2,415	11 fixed pts	44 cycles	14 nodes	2.60 avg steps	9 max steps	7.89 avg steps	19 max steps	171 final numbers
69	2,485	11 fixed pts	79 cycles	33 nodes	1.10 avg steps	4 max steps	15.92 avg steps	37 max steps	561 final numbers
70	2,556	11 fixed pts	46 cycles	14 nodes	2.63 avg steps	9 max steps	7.80 avg steps	19 max steps	179 final numbers
71	2,628	12 fixed pts	82 cycles	33 nodes	1.10 avg steps	4 max steps	15.30 avg steps	35 max steps	595 final numbers
72	2,701	11 fixed pts	49 cycles	14 nodes	2.53 avg steps	9 max steps	8.23 avg steps	19 max steps	196 final numbers
73	2,775	12 fixed pts	83 cycles	35 nodes	1.09 avg steps	4 max steps	17.27 avg steps	39 max steps	630 final numbers
74	2,850	12 fixed pts	51 cycles	14 nodes	2.67 avg steps	9 max steps	7.85 avg steps	19 max steps	200 final numbers
75	2,926	12 fixed pts	87 cycles	35 nodes	1.09 avg steps	4 max steps	15.59 avg steps	37 max steps	666 final numbers
76	3,003	12 fixed pts	52 cycles	18 nodes	2.52 avg steps	9 max steps	9.18 avg steps	23 max steps	218 final numbers
77	3,081	13 fixed pts	92 cycles	35 nodes	1.09 avg steps	4 max steps	15.84 avg steps	37 max steps	703 final numbers
78	3,160	12 fixed pts	53 cycles	18 nodes	2.54 avg steps	9 max steps	8.88 avg steps	23 max steps	227 final numbers
79	3,240	13 fixed pts	95 cycles	35 nodes	1.09 avg steps	4 max steps	16.82 avg steps	37 max steps	741 final numbers
80	3,321	13 fixed pts	56 cycles	18 nodes	2.46 avg steps	9 max steps	9.00 avg steps	23 max steps	246 final numbers
81	3,403	13 fixed pts	96 cycles	39 nodes	1.09 avg steps	4 max steps	18.60 avg steps	43 max steps	780 final numbers
82	3,486	13 fixed pts	57 cycles	18 nodes	2.73 avg steps	10 max steps	8.69 avg steps	23 max steps	248 final numbers
83	3,570	14 fixed pts	100 cycles	39 nodes	1.08 avg steps	4 max steps	17.91 avg steps	41 max steps	820 final numbers
84	3,655	13 fixed pts	59 cycles	18 nodes	2.50 avg steps	9 max steps	9.08 avg steps	23 max steps	268 final numbers
85	3,741	14 fixed pts	101 cycles	41 nodes	1.08 avg steps	4 max steps	19.91 avg steps	45 max steps	861 final numbers
86	3,828	14 fixed pts	62 cycles	18 nodes	2.52 avg steps	9 max steps	8.78 avg steps	23 max steps	278 final numbers
87	3,916	14 fixed pts	108 cycles	41 nodes	1.08 avg steps	4 max steps	17.90 avg steps	43 max steps	903 final numbers
88	4,005	14 fixed pts	65 cycles	18 nodes	2.45 avg steps	9 max steps	8.84 avg steps	23 max steps	299 final numbers
89	4,095	15 fixed pts	111 cycles	41 nodes	1.08 avg steps	4 max steps	18.85 avg steps	43 max steps	946 final numbers
90	4,186	14 fixed pts	66 cycles	18 nodes	2.56 avg steps	9 max steps	8.80 avg steps	23 max steps	304 final numbers
91	4,278	15 fixed pts	115 cycles	41 nodes	1.08 avg steps	4 max steps	18.05 avg steps	43 max steps	990 final numbers
92	4,371	15 fixed pts	71 cycles	18 nodes	2.44 avg steps	9 max steps	8.91 avg steps	23 max steps	326 final numbers
93	4,465	15 fixed pts	120 cycles	41 nodes	1.07 avg steps	4 max steps	17.77 avg steps	43 max steps	1,035 final numbers
94	4,560	15 fixed pts	72 cycles	18 nodes	2.47 avg steps	9 max steps	9.24 avg steps	23 max steps	337 final numbers
95	4,656	16 fixed pts	127 cycles	41 nodes	1.07 avg steps	4 max steps	17.32 avg steps	43 max steps	1,081 final numbers
96	4,753	15 fixed pts	73 cycles	23 nodes	2.40 avg steps	9 max steps	10.33 avg steps	27 max steps	360 final numbers
97	4,851	16 fixed pts	130 cycles	41 nodes	1.07 avg steps	4 max steps	18.70 avg steps	43 max steps	1,128 final numbers
98	4,950	16 fixed pts	74 cycles	23 nodes	2.78 avg steps	12 max steps	9.56 avg steps	27 max steps	361 final numbers
99	5,050	16 fixed pts	132 cycles	41 nodes	1.07 avg steps	4 max steps	18.73 avg steps	43 max steps	1,176 final numbers
100	5,151	16 fixed pts	76 cycles	23 nodes	2.48 avg steps	9 max steps	10.66 avg steps	28 max steps	385 final numbers