Base 10: 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] [8] [9] [Base 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	8	9

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	13	14
1	0 cycles	-	-	-	-	-	-	-	-	-	-	-	-	-	-
2	1 cycle	-	-	-	-	45×	-	-	-	-	-	-	-	-	-
3	1 cycle	210×	-	-	-	-	-	-	-	-	-	-	-	-	-
4	1 cycle	705×	-	-	-	-	-	-	-	-	-	-	-	-	-
5	3 cycles	-	108×	-	1,884×	-	-	-	-	-	-	-	-	-	-
6	3 cycles	382×	-	-	-	-	-	4,613×	-	-	-	-	-	-	-
7	1 cycle	-	-	-	-	-	-	-	11,430×	-	-	-	-	-	-
8	4 cycles	621×	-	12,051×	-	-	-	11,628×	-	-	-	-	-	-	-
9	3 cycles	2,418×	-	-	-	-	-	-	-	-	-	-	-	-	46,192×
10	8 cycles	6,151×	-	64,634×	-	-	-	21,583×	-	-	-	-	-	-	-
11	3 cycles	9,432×	-	-	-	105,384×	-	-	53,134×	-	-	-	-	-	-
12	16 cycles	6,979×	-	234,788×	-	-	-	52,153×	-	-	-	-	-	-	-
13	5 cycles	9,172×	46,384×	-	-	441,854×	-	-	-	-	-	-	-	-	-
14	27 cycles	31,257×	-	671,493×	-	-	-	114,430×	-	-	-	-	-	-	-
15	8 cycles	6,556×	34,062×	-	-	1,266,876×	-	-	-	-	-	-	-	-	-
16	46 cycles	53,473×	22,116×	1,654,149×	-	-	-	313,227×	-	-	-	-	-	-	-
17	9 cycles	55,360×	43,784×	-	-	3,025,396×	-	-	-	-	-	-	-	-	-
18	73 cycles	386,507×	-	3,707,218×	-	-	-	593,090×	-	-	-	-	-	-	-
19	11 cycles	2,384,212×	47,390×	295,858×	-	4,179,430×	-	-	-	-	-	-	-	-	-
20	110 cycles	735,409×	-	7,903,501×	-	659,020×	-	717,065×	-	-	-	-	-	-	-
21	16 cycles	4,875,598×	53,562×	5,666,956×	-	3,711,024×	-	-	-	-	-	-	-	-	-
22	162 cycles	750,095×	-	14,306,576×	-	4,217,036×	-	886,358×	-	-	-	-	-	-	-
23	25 cycles	5,035,912×	107,832×	19,122,002×	-	3,783,044×	-	-	-	-	-	-	-	-	-
24	231 cycles	1,073,855×	-	25,614,889×	-	10,961,281×	-	917,065×	-	-	-	-	-	-	-
25	37 cycles	6,420,608×	259,492×	42,285,906×	-	3,485,240×	-	-	-	-	-	-	-	-	-
26	318 cycles	2,213,846×	-	43,756,390×	-	23,544,832×	-	1,092,382×	-	-	-	-	-	-	-
27	58 cycles	8,786,694×	72,206×	81,531,504×	-	3,752,866×	-	-	-	-	-	-	-	-	-
28	429 cycles	21,074,683×	-	75,509,466×	-	26,312,355×	-	1,507,106×	-	-	-	-	-	-	-
29	88 cycles	12,264,702×	83,986×	142,720,980×	-	7,941,962×	-	-	-	-	-	-	-	-	-
30	572 cycles	33,492,534×	221,372×	159,077,720×	-	17,407,499×	-	1,715,997×	-	-	-	-	-	-	-
31	132 cycles	11,749,564×	86,886×	231,096,836×	-	30,505,584×	-	-	-	-	-	-	-	-	-
32	747 cycles	28,111,602×	318,564×	303,415,543×	-	16,824,140×	-	1,673,706×	-	-	-	-	-	-	-
33	192 cycles	14,341,490×	98,628×	366,876,420×	-	64,575,262×	-	-	-	-	-	-	-	-	-
34	963 cycles	33,851,370×	1,035,730×	511,080,652×	-	15,663,798×	-	2,290,435×	-	-	-	-	-	-	-
35	269 cycles	21,590,806×	101,006×	562,865,406×	-	124,373,280×	-	-	-	-	-	-	-	-	-
36	1,229 cycles	46,891,227×	-	819,948,824×	-	15,820,016×	-	3,503,058×	-	-	-	-	-	-	-
37	372 cycles	114,570,838×	462,252×	868,361,490×	-	118,321,740×	-	-	-	-	-	-	-	-	-
38	1,551 cycles	65,400,039×	-	1,259,879,815×	-	33,042,508×	-	4,326,773×	-	-	-	-	-	-	-
39	500 cycles	161,762,478×	795,582×	1,446,799,588×	-	67,748,982×	-	-	-	-	-	-	-	-	-
40	1,939 cycles	53,042,153×	-	1,867,214,562×	-	128,789,030×	-	5,409,879×	-	-	-	-	-	-	-
41	662 cycles	121,113,748×	1,905,296×	2,317,996,606×	-	64,418,040×	-	-	-	-	-	-	-	-	-
42	2,401 cycles	59,873,917×	-	2,723,158,729×	-	252,258,194×	-	7,021,500×	-	-	-	-	-	-	-
43	864 cycles	142,732,666×	4,795,788×	3,476,378,092×	-	55,168,844×	-	-	-	-	-	-	-	-	-
44	2,948 cycles	83,575,568×	705,380×	3,877,826,253×	-	461,558,168×	-	7,948,171×	-	-	-	-	-	-	-
45	1,115 cycles	185,161,980×	145,018×	5,075,080,470×	-	57,548,782×	-	-	-	-	-	-	-	-	-
46	3,586 cycles	419,597,949×	1,133,822×	5,507,605,190×	-	422,620,616×	-	7,444,463×	-	-	-	-	-	-	-
47	1,421 cycles	260,748,474×	144,678×	7,213,527,984×	-	101,547,254×	-	-	-	-	-	-	-	-	-
48	4,330 cycles	576,030,788×	3,036,618×	8,204,302,135×	-	202,369,824×	-	10,723,100×	-	-	-	-	-	-	-
49	1,792 cycles	208,483,834×	159,300×	10,028,450,780×	-	411,780,026×	-	-	-	-	-	-	-	-	-
50	5,194 cycles	384,383,964×	6,841,050×	11,977,846,094×	-	183,472,298×	-	13,127,845×	-	-	-	-	-	-	-
51	2,240 cycles	222,474,376×	1,305,800×	13,763,201,768×	-	796,160,706×	-	-	-	-	-	-	-	-	-
52	6,191 cycles	449,417,086×	14,114,390×	16,702,071,991×	-	161,168,770×	-	14,991,258×	-	-	-	-	-	-	-
53	2,764 cycles	288,399,090×	2,223,964×	18,613,845,976×	-	1,382,122,230×	-	-	-	-	-	-	-	-	-
54	7,338 cycles	590,541,148×	-	22,896,086,020×	-	163,704,096×	-	17,358,541×	-	-	-	-	-	-	-
55	3,382 cycles	1,270,164,314×	4,584,590×	25,067,100,472×	-	1,198,735,126×	-	-	-	-	-	-	-	-	-
56	8,650 cycles	827,234,745×	-	30,834,734,675×	-	279,816,230×	-	24,964,220×	-	-	-	-	-	-	-
57	4,105 cycles	1,671,313,498×	10,588,332×	34,797,593,950×	-	534,635,650×	-	-	-	-	-	-	-	-	-
58	10,149 cycles	630,864,938×	2,042,394×	40,945,293,951×	-	1,154,795,126×	-	24,707,141×	-	-	-	-	-	-	-
59	4,947 cycles	1,095,979,248×	20,810,776×	47,705,816,052×	-	457,459,034×	-	-	-	-	-	-	-	-	-
60	11,844 cycles	674,519,811×	2,733,474×	53,866,332,571×	-	2,100,490,254×	-	27,998,768×	-	-	-	-	-	-	-
61	5,921 cycles	1,230,949,894×	33,803,250×	63,371,596,398×	-	397,179,008×	-	-	-	-	-	-	-	-	-
62	13,756 cycles	832,428,393×	6,340,488×	70,021,119,442×	-	3,581,277,582×	-	32,713,565×	-	-	-	-	-	-	-
63	7,044 cycles	1,567,451,484×	202,470×	83,148,646,690×	-	396,704,466×	-	-	-	-	-	-	-	-	-
64	15,908 cycles	3,312,133,045×	15,174,302×	90,714,536,242×	-	3,004,309,482×	-	35,868,384×	-	-	-	-	-	-	-
65	8,336 cycles	2,199,890,474×	2,964,688×	107,685,557,220×	-	635,735,122×	-	-	-	-	-	-	-	-	-
66	18,321 cycles	4,247,072,879×	29,846,752×	120,043,149,935×	-	1,232,542,838×	-	43,009,761×	-	-	-	-	-	-	-
67	9,804 cycles	1,667,180,968×	4,401,850×	138,032,155,742×	-	2,762,937,330×	-	-	-	-	-	-	-	-	-
68	21,020 cycles	2,649,558,744×	45,535,870×	157,534,750,733×	-	1,046,725,006×	-	45,989,112×	-	-	-	-	-	-	-
69	11,472 cycles	1,762,841,806×	8,658,490×	175,688,062,072×	-	4,905,070,072×	-	-	-	-	-	-	-	-	-
70	24,028 cycles	2,963,260,621×	73,541,380×	201,808,739,557×	-	904,941,664×	-	61,030,533×	-	-	-	-	-	-	-
71	13,356 cycles	2,090,567,454×	20,589,906×	221,680,477,302×	-	8,108,662,528×	-	-	-	-	-	-	-	-	-
72	27,378 cycles	3,771,118,652×	4,216,668×	256,146,955,196×	-	892,006,628×	-	73,537,196×	-	-	-	-	-	-	-
73	15,479 cycles	7,590,293,974×	39,762,448×	278,842,106,702×	-	6,579,924,766×	-	-	-	-	-	-	-	-	-
74	31,087 cycles	5,365,870,484×	5,901,864×	321,887,507,721×	-	1,365,138,458×	-	69,139,513×	-	-	-	-	-	-	-
75	17,862 cycles	9,542,757,712×	61,263,086×	355,851,453,510×	-	2,681,310,698×	-	-	-	-	-	-	-	-	-
76	35,188 cycles	4,009,037,914×	12,464,390×	401,472,680,116×	-	6,161,330,068×	-	76,418,112×	-	-	-	-	-	-	-
77	20,530 cycles	6,129,455,020×	95,403,516×	451,426,313,484×	-	2,205,269,950×	-	-	-	-	-	-	-	-	-
78	39,712 cycles	4,186,491,638×	26,120,178×	498,149,120,721×	-	10,469,580,422×	-	85,487,701×	-	-	-	-	-	-	-
79	23,512 cycles	6,491,258,300×	159,172,636×	562,858,235,738×	-	1,841,693,556×	-	-	-	-	-	-	-	-	-