Base 4: Cycles Lengths: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets]
[Odd Digit Sets]
[Even Digit Sets]
Final Numbers
[Fixed Points]
Cycles Lengths
[All Digit Sets] — [2] [3] [Base 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]
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	3

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	# Full Cycles (excluding zero)	Nodes
Digits	# Full Cycles (excluding zero)	1	2	3
1	0 cycles	-	-	-
2	1 cycle	-	6×	-
3	1 cycle	16×	-	-
4	2 cycles	9×	22×	-
5	1 cycle	-	52×	-
6	3 cycles	80×	-	-
7	1 cycle	116×	-	-
8	4 cycles	61×	-	100×
9	3 cycles	216×	-	-
10	5 cycles	282×	-	-
11	4 cycles	192×	-	168×
12	8 cycles	451×	-	-
13	5 cycles	556×	-	-
14	10 cycles	434×	-	242×
15	8 cycles	812×	-	-
16	12 cycles	965×	-	-
17	10 cycles	992×	-	144×
18	16 cycles	1,326×	-	-
19	12 cycles	1,536×	-	-
20	19 cycles	1,583×	-	184×
21	16 cycles	2,020×	-	-
22	22 cycles	2,296×	-	-
23	19 cycles	2,406×	-	190×
24	27 cycles	2,921×	-	-
25	22 cycles	3,272×	-	-
26	31 cycles	3,414×	-	236×
27	27 cycles	4,056×	-	-
28	35 cycles	4,491×	-	-
29	31 cycles	4,732×	-	224×
30	41 cycles	5,452×	-	-
31	35 cycles	5,980×	-	-
32	46 cycles	6,279×	-	262×
33	41 cycles	7,136×	-	-
34	51 cycles	7,766×	-	-
35	46 cycles	8,162×	-	270×
36	58 cycles	9,135×	-	-
37	51 cycles	9,876×	-	-
38	64 cycles	10,324×	-	332×
39	58 cycles	11,476×	-	-
40	70 cycles	12,337×	-	-
41	64 cycles	12,930×	-	310×
42	78 cycles	14,186×	-	-
43	70 cycles	15,176×	-	-
44	85 cycles	15,849×	-	362×
45	78 cycles	17,292×	-	-
46	92 cycles	18,420×	-	-
47	85 cycles	19,252×	-	344×
48	101 cycles	20,821×	-	-
49	92 cycles	22,096×	-	-
50	109 cycles	22,990×	-	432×
51	101 cycles	24,800×	-	-
52	117 cycles	26,231×	-	-
53	109 cycles	27,332×	-	384×
54	127 cycles	29,256×	-	-
55	117 cycles	30,852×	-	-
56	136 cycles	32,061×	-	444×
57	127 cycles	34,216×	-	-
58	145 cycles	35,986×	-	-
59	136 cycles	37,392×	-	424×
60	156 cycles	39,707×	-	-
61	145 cycles	41,660×	-	-
62	166 cycles	43,170×	-	506×
63	156 cycles	45,756×	-	-
64	176 cycles	47,901×	-	-
65	166 cycles	49,648×	-	464×
66	188 cycles	52,390×	-	-
67	176 cycles	54,736×	-	-
68	199 cycles	56,613×	-	538×
69	188 cycles	59,636×	-	-
70	210 cycles	62,192×	-	-
71	199 cycles	64,316×	-	504×
72	223 cycles	67,521×	-	-
73	210 cycles	70,296×	-	-
74	235 cycles	72,522×	-	624×
75	223 cycles	76,072×	-	-
76	247 cycles	79,075×	-	-
77	235 cycles	81,612×	-	544×
78	261 cycles	85,316×	-	-
79	247 cycles	88,556×	-	-
80	274 cycles	91,251×	-	626×
81	261 cycles	95,280×	-	-
82	287 cycles	98,766×	-	-
83	274 cycles	101,752×	-	584×
84	302 cycles	105,991×	-	-
85	287 cycles	109,732×	-	-
86	316 cycles	112,858×	-	702×
87	302 cycles	117,476×	-	-
88	330 cycles	121,481×	-	-
89	316 cycles	124,952×	-	624×
90	346 cycles	129,762×	-	-
91	330 cycles	134,040×	-	-
92	361 cycles	137,703×	-	708×
93	346 cycles	142,876×	-	-
94	376 cycles	147,436×	-	-
95	361 cycles	151,428×	-	664×
96	393 cycles	156,845×	-	-
97	376 cycles	161,696×	-	-
98	409 cycles	165,826×	-	820×
99	393 cycles	171,696×	-	-
100	425 cycles	176,847×	-	-