Base 3: Summary: Even Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets]
[Odd Digit Sets]
[Even 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]
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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