Base 9: Cycles Lengths: Even 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]
[Odd Digit Sets]
[Even Digit Sets] — [2] [3] [4] [5] [6] [7] [8] [Base 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]
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

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	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
2	1 cycle	-	32×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
4	2 cycles	-	-	486×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
6	1 cycle	-	-	-	-	-	-	-	-	-	-	-	-	-	2,994×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
8	2 cycles	200×	-	-	12,661×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
10	3 cycles	441×	-	-	36,148×	7,160×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
12	3 cycles	-	112,701×	-	-	-	13,260×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
14	3 cycles	4,608×	-	-	-	-	-	-	-	-	-	315,153×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
16	2 cycles	264×	735,198×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
18	4 cycles	22,701×	-	-	-	-	348,611×	-	-	1,190,954×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
20	4 cycles	1,184×	-	-	-	-	22,678×	-	-	-	-	-	-	-	-	3,084,234×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
22	5 cycles	408×	186,351×	-	-	-	-	-	-	-	5,666,157×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
24	4 cycles	21,134×	8,698,985×	-	-	-	1,798,172×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
26	4 cycles	984×	8,370,211×	-	-	-	-	-	-	-	-	-	-	9,785,000×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
28	5 cycles	7,032×	-	-	-	-	1,022,355×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	29,230,944×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
30	5 cycles	1,696×	-	-	-	-	-	18,621,201×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	30,280,586×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
32	7 cycles	6,862,244×	14,434,970×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	55,607,462×	-	-	-	-	-	-	-	-	-	-	-
34	5 cycles	792,204×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	117,237,972×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
36	6 cycles	841,156×	-	-	52,547,856×	-	-	-	-	123,843,606×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
38	8 cycles	743,212×	-	-	8,302,635×	-	-	251,886,959×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
40	8 cycles	736,564×	-	-	8,302,635×	-	41,291,458×	221,623,229×	-	-	-	-	-	-	-	-	-	-	-	-	-	105,395,099×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
42	11 cycles	752,888×	45,500×	-	8,302,635×	-	-	72,353,422×	-	200,718,378×	-	-	-	-	-	-	204,969,840×	-	-	-	-	-	49,735,978×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
44	11 cycles	839,660×	9,697,631×	44,786,963×	8,302,635×	17,033,005×	-	12,571,741×	659,306,506×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
46	12 cycles	756,052×	4,012,308×	7,395,002×	8,302,635×	-	-	12,571,741×	26,886,569×	-	-	-	-	-	253,315,232×	-	-	-	-	-	-	-	727,226,242×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
48	14 cycles	755,624×	897,611,263×	142,972,052×	8,302,635×	130,671,653×	200,722,529×	12,571,741×	26,886,569×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
50	15 cycles	754,516×	68,072,056×	17,480,311×	8,302,635×	-	45,657,212×	12,571,741×	26,886,569×	-	-	-	-	-	-	-	-	-	-	-	-	1,737,072,262×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
52	17 cycles	757,144×	68,139,684×	17,480,311×	1,251,213,764×	106,340,977×	45,657,212×	12,571,741×	26,886,569×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	1,029,573,434×	-	-	-	-	-	-	-	-	-	-	-
54	19 cycles	1,162,752×	68,072,056×	17,480,311×	60,972,856×	13,242,826×	45,657,212×	1,834,815,850×	26,886,569×	-	-	-	-	1,312,808,104×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
56	22 cycles	776,796×	68,072,056×	17,480,311×	60,972,856×	1,334,160,212×	45,657,212×	914,489,981×	1,522,396,262×	-	462,159,673×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
58	22 cycles	756,124×	68,072,056×	17,480,311×	60,972,856×	33,369,626×	673,690,871×	209,592,935×	164,861,284×	116,013,844×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	4,398,762,204×	-	-	-	-	-	-
60	21 cycles	756,288×	68,072,056×	17,480,311×	60,972,856×	544,858,060×	45,657,212×	209,592,935×	6,444,620,041×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
62	23 cycles	8,296,568,869×	68,169,836×	17,480,311×	60,972,856×	142,185,553×	45,657,212×	209,592,935×	599,723,339×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
64	29 cycles	198,741,878×	68,072,056×	17,480,311×	60,972,856×	3,391,879,376×	632,705,855×	309,775,520×	599,723,339×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	6,689,665,145×
66	26 cycles	198,474,254×	68,072,056×	17,480,311×	60,972,856×	430,156,423×	45,657,212×	209,592,935×	599,723,339×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	13,441,345,266×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
68	34 cycles	198,490,842×	68,072,056×	17,480,311×	60,972,856×	11,939,004,446×	45,657,212×	209,592,935×	599,723,339×	-	-	-	-	-	-	-	-	-	-	-	-	5,716,889,569×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
70	34 cycles	198,464,946×	68,072,056×	17,480,311×	12,917,724,685×	1,336,773,122×	45,657,212×	209,592,935×	8,653,116,039×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
72	36 cycles	199,075,234×	68,201,244×	17,480,311×	2,385,786,898×	1,336,773,122×	45,657,212×	209,592,935×	599,723,339×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	24,125,246,846×	-	-	-	-	-	-	-	-	-
74	39 cycles	198,917,002×	68,072,056×	17,480,311×	1,382,645,989×	1,336,773,122×	45,657,212×	19,086,579,411×	13,399,775,271×	-	105,569,767×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
76	37 cycles	198,509,178×	68,072,056×	17,480,311×	4,346,661,613×	1,364,077,121×	45,657,212×	209,592,935×	599,723,339×	-	-	-	-	-	-	36,745,371,820×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
78	38 cycles	198,501,970×	68,072,056×	17,480,311×	1,918,708,749×	1,336,773,122×	45,657,212×	47,451,868,178×	599,723,339×	-	-	-	-	-	-	1,423,573,744×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-