Base 8: 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] [4] [5] [6] [7] [Base 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	4	5	6	7

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	4	5	6	7	8	9	10	11	12
1	0 cycles	-	-	-	-	-	-	-	-	-	-	-	-
2	2 cycles	7×	-	21×	-	-	-	-	-	-	-	-	-
3	1 cycle	112×	-	-	-	-	-	-	-	-	-	-	-
4	2 cycles	-	-	92×	-	230×	-	-	-	-	-	-	-
5	2 cycles	-	70×	-	714×	-	-	-	-	-	-	-	-
6	3 cycles	1,472×	-	236×	-	-	-	-	-	-	-	-	-
7	3 cycles	334×	-	-	340×	-	-	2,750×	-	-	-	-	-
8	3 cycles	325×	-	6,102×	-	-	-	-	-	-	-	-	-
9	4 cycles	20×	-	-	8,202×	3,210×	-	-	-	-	-	-	-
10	5 cycles	95×	-	19,345×	-	-	-	-	-	-	-	-	-
11	3 cycles	-	10,034×	-	7,882×	-	13,900×	-	-	-	-	-	-
12	13 cycles	6,791×	686×	39,541×	3,362×	-	-	-	-	-	-	-	-
13	2 cycles	-	-	-	-	17,094×	-	-	-	60,418×	-	-	-
14	16 cycles	12,126×	-	104,146×	-	-	-	-	-	-	-	-	-
15	3 cycles	50,562×	-	-	-	-	-	-	-	-	-	-	119,974×
16	21 cycles	2,568×	-	242,581×	-	-	-	-	-	-	-	-	-
17	5 cycles	2,180×	856×	270,102×	-	72,958×	-	-	-	-	-	-	-
18	34 cycles	8,111×	40,592×	368,375×	-	-	63,614×	-	-	-	-	-	-
19	5 cycles	9,868×	-	647,924×	-	-	-	-	-	-	-	-	-
20	45 cycles	31,613×	-	572,477×	-	60,474×	-	-	-	223,458×	-	-	-
21	12 cycles	226,104×	-	957,928×	-	-	-	-	-	-	-	-	-
22	62 cycles	183,373×	1,682×	935,385×	-	-	-	-	-	-	-	-	440,332×
23	13 cycles	14,614×	-	2,021,178×	-	-	-	-	-	-	-	-	-
24	82 cycles	54,934×	-	2,306,837×	-	267,796×	-	-	-	-	-	-	-
25	22 cycles	14,614×	115,138×	2,995,132×	-	-	240,964×	-	-	-	-	-	-
26	104 cycles	96,770×	-	4,175,270×	-	-	-	-	-	-	-	-	-
27	35 cycles	188,394×	964×	4,280,050×	-	241,936×	-	-	-	668,264×	-	-	-
28	137 cycles	769,720×	-	5,954,792×	-	-	-	-	-	-	-	-	-
29	45 cycles	573,806×	-	6,410,570×	-	-	-	-	-	-	-	-	1,363,296×
30	170 cycles	115,779×	-	10,179,685×	-	-	-	-	-	-	-	-	-
31	61 cycles	160,896×	-	11,685,414×	-	773,938×	-	-	-	-	-	-	-
32	215 cycles	191,499×	226,468×	14,193,510×	-	-	769,452×	-	-	-	-	-	-
33	82 cycles	348,746×	-	18,294,806×	-	-	-	-	-	-	-	-	-
34	264 cycles	508,471×	-	19,692,635×	-	712,002×	-	-	-	1,568,824×	-	-	-
35	111 cycles	1,714,828×	-	25,263,492×	-	-	-	-	-	-	-	-	-
36	323 cycles	1,541,948×	-	27,464,588×	-	-	-	-	-	-	-	-	3,217,570×
37	139 cycles	257,024×	1,244×	38,062,292×	-	-	-	-	-	-	-	-	-
38	389 cycles	598,076×	-	42,712,092×	-	2,069,444×	-	-	-	-	-	-	-
39	179 cycles	716,718×	443,436×	50,494,082×	-	-	1,870,436×	-	-	-	-	-	-
40	466 cycles	847,986×	-	62,043,505×	-	-	-	-	-	-	-	-	-
41	223 cycles	879,600×	-	67,589,294×	-	1,633,574×	-	-	-	3,526,596×	-	-	-
42	564 cycles	4,265,627×	2,026×	81,632,923×	-	-	-	-	-	-	-	-	-
43	275 cycles	3,238,200×	-	89,658,246×	-	-	-	-	-	-	-	-	6,987,946×
44	657 cycles	916,515×	-	114,858,577×	-	-	-	-	-	-	-	-	-
45	338 cycles	1,407,662×	-	128,252,818×	-	4,124,072×	-	-	-	-	-	-	-
46	774 cycles	1,623,247×	717,816×	147,525,915×	-	-	4,276,094×	-	-	-	-	-	-
47	410 cycles	1,419,724×	1,596×	175,679,232×	-	-	-	-	-	-	-	-	-
48	905 cycles	1,957,398×	-	190,176,831×	-	3,554,656×	-	-	-	7,238,832×	-	-	-
49	498 cycles	7,773,544×	-	224,143,848×	-	-	-	-	-	-	-	-	-
50	1,048 cycles	7,388,726×	-	243,347,560×	-	-	-	-	-	-	-	-	13,649,542×
51	587 cycles	1,942,380×	-	298,731,700×	-	-	-	-	-	-	-	-	-
52	1,212 cycles	3,029,628×	2,492×	329,842,200×	-	8,275,118×	-	-	-	-	-	-	-
53	696 cycles	2,327,400×	1,235,406×	373,858,748×	-	-	8,785,358×	-	-	-	-	-	-
54	1,392 cycles	3,632,625×	-	432,638,147×	-	-	-	-	-	-	-	-	-
55	818 cycles	2,858,160×	-	468,358,298×	-	6,736,178×	-	-	-	13,843,508×	-	-	-
56	1,598 cycles	15,739,679×	-	537,530,984×	-	-	-	-	-	-	-	-	-
57	958 cycles	13,517,234×	1,948×	582,765,684×	-	-	-	-	-	-	-	-	24,931,318×
58	1,811 cycles	4,587,213×	-	691,603,339×	-	-	-	-	-	-	-	-	-
59	1,110 cycles	4,368,488×	-	760,076,950×	-	14,343,994×	-	-	-	-	-	-	-
60	2,058 cycles	5,480,834×	1,939,430×	845,365,942×	-	-	16,861,994×	-	-	-	-	-	-
61	1,281 cycles	4,695,184×	-	964,748,712×	-	-	-	-	-	-	-	-	-
62	2,326 cycles	6,825,446×	2,988×	1,035,842,780×	-	11,776,830×	-	-	-	24,449,196×	-	-	-
63	1,482 cycles	23,975,050×	-	1,174,799,662×	-	-	-	-	-	-	-	-	-
64	2,617 cycles	25,936,240×	-	1,261,600,789×	-	-	-	-	-	-	-	-	42,353,668×
65	1,684 cycles	5,635,704×	-	1,467,473,992×	-	-	-	-	-	-	-	-	-
66	2,938 cycles	9,243,213×	-	1,594,571,777×	-	25,533,614×	-	-	-	-	-	-	-
67	1,922 cycles	7,134,662×	2,656,264×	1,759,944,326×	-	-	29,843,804×	-	-	-	-	-	-
68	3,284 cycles	10,152,475×	-	1,974,677,367×	-	-	-	-	-	-	-	-	-
69	2,180 cycles	9,995,072×	-	2,115,284,706×	-	20,144,940×	-	-	-	40,764,674×	-	-	-
70	3,672 cycles	45,830,311×	-	2,358,978,021×	-	-	-	-	-	-	-	-	-
71	2,461 cycles	41,139,472×	-	2,532,871,130×	-	-	-	-	-	-	-	-	67,891,510×
72	4,076 cycles	11,908,390×	3,484×	2,886,841,833×	-	-	-	-	-	-	-	-	-
73	2,770 cycles	11,331,214×	-	3,125,921,172×	-	39,464,006×	-	-	-	-	-	-	-
74	4,520 cycles	16,298,470×	3,942,420×	3,406,855,708×	-	-	50,119,994×	-	-	-	-	-	-
75	3,108 cycles	14,207,000×	-	3,787,549,808×	-	-	-	-	-	-	-	-	-
76	5,000 cycles	19,277,672×	-	4,035,017,006×	-	32,342,684×	-	-	-	65,281,258×	-	-	-
77	3,487 cycles	61,937,234×	2,652×	4,467,425,882×	-	-	-	-	-	-	-	-	-
78	5,518 cycles	72,617,311×	-	4,757,696,715×	-	-	-	-	-	-	-	-	105,533,286×
79	3,874 cycles	14,620,250×	-	5,358,580,622×	-	-	-	-	-	-	-	-	-
80	6,073 cycles	23,078,363×	-	5,756,913,280×	-	63,364,306×	-	-	-	-	-	-	-
81	4,310 cycles	21,319,998×	5,677,464×	6,241,008,794×	-	-	80,331,072×	-	-	-	-	-	-
82	6,672 cycles	27,654,467×	3,980×	6,862,610,117×	-	-	-	-	-	-	-	-	-
83	4,777 cycles	23,476,830×	-	7,293,591,382×	-	47,033,280×	-	-	-	107,274,060×	-	-	-
84	7,325 cycles	102,954,360×	-	7,991,035,822×	-	-	-	-	-	-	-	-	-
85	5,281 cycles	102,817,438×	-	8,496,086,770×	-	-	-	-	-	-	-	-	161,649,872×
86	7,998 cycles	31,492,958×	-	9,442,129,478×	-	-	-	-	-	-	-	-	-
87	5,828 cycles	28,964,190×	3,004×	10,117,798,384×	-	89,102,342×	-	-	-	-	-	-	-
88	8,734 cycles	38,576,078×	7,158,728×	10,876,016,649×	-	-	128,333,232×	-	-	-	-	-	-
89	6,410 cycles	30,533,654×	-	11,888,658,818×	-	-	-	-	-	-	-	-	-
90	9,519 cycles	43,576,403×	-	12,569,479,395×	-	71,058,552×	-	-	-	162,126,426×	-	-	-
91	7,050 cycles	136,491,198×	-	13,697,921,946×	-	-	-	-	-	-	-	-	-
92	10,354 cycles	172,002,895×	4,476×	14,481,592,943×	-	-	-	-	-	-	-	-	233,431,222×
93	7,711 cycles	36,692,096×	-	15,970,868,696×	-	-	-	-	-	-	-	-	-
94	11,242 cycles	54,958,745×	-	17,008,657,009×	-	135,997,438×	-	-	-	-	-	-	-
95	8,432 cycles	43,067,868×	8,894,750×	18,220,285,638×	-	-	194,704,856×	-	-	-	-	-	-
96	12,188 cycles	58,818,590×	-	19,754,683,187×	-	-	-	-	-	-	-	-	-
97	9,203 cycles	47,662,870×	3,356×	20,853,666,214×	-	102,967,644×	-	-	-	239,042,028×	-	-	-
98	13,204 cycles	224,643,480×	-	22,536,080,212×	-	-	-	-	-	-	-	-	-
99	10,023 cycles	237,791,426×	-	23,794,311,836×	-	-	-	-	-	-	-	-	337,964,530×
100	14,255 cycles	70,709,368×	-	26,005,263,170×	-	-	-	-	-	-	-	-	-