Base 9: Cycles Lengths: Odd 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] — [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]
[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

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	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65
1	0 cycles	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
3	1 cycle	-	156×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
5	2 cycles	93×	-	-	-	1,185×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
7	1 cycle	-	6,426×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
9	2 cycles	3,013×	-	-	-	-	-	-	-	-	-	-	21,288×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
11	2 cycles	216×	-	-	-	-	75,357×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
13	3 cycles	192×	-	-	175,626×	-	27,663×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
15	4 cycles	508×	-	52,473×	349,818×	-	87,506×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
17	4 cycles	408,450×	8,012×	-	-	-	-	665,104×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
19	5 cycles	63,782×	-	-	2,156,284×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
21	6 cycles	52,841×	-	-	246,219×	-	2,314,027×	1,679,049×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
23	9 cycles	56,245×	290,085×	394,019×	119,309×	-	-	409,389×	6,619,669×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
25	15 cycles	53,769×	5,127,292×	1,108,412×	1,221,227×	-	4,072,037×	1,353,449×	947,961×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
27	15 cycles	118,314×	910,846×	348,582×	1,589,598×	1,381,840×	738,683×	409,389×	947,961×	-	-	-	-	-	-	-	-	-	-	-	17,090,598×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
29	18 cycles	86,557×	893,881×	547,667×	850,477×	1,655,760×	738,683×	7,115,941×	26,719,045×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
31	19 cycles	53,609×	893,881×	988,199×	850,477×	13,724,371×	738,683×	2,638,649×	41,635,870×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
33	23 cycles	59,797×	893,881×	348,582×	850,477×	13,253,004×	738,683×	2,638,649×	13,851,132×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	62,914,031×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
35	30 cycles	55,041×	893,881×	348,582×	850,477×	112,344,560×	738,683×	2,638,649×	27,138,631×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
37	32 cycles	60,321×	926,057×	348,582×	25,599,065×	17,380,453×	738,683×	2,638,649×	13,851,132×	-	-	-	-	-	-	-	-	-	154,010,244×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
39	32 cycles	128,573×	893,881×	348,582×	43,393,842×	17,380,453×	738,683×	2,638,649×	13,851,132×	-	-	-	-	-	-	59,662,178×	-	-	175,421,513×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
41	34 cycles	70,725×	893,881×	348,582×	22,639,105×	17,380,453×	738,683×	2,638,649×	13,851,132×	-	-	-	-	6,122,998×	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	374,901,812×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
43	34 cycles	64,701×	893,881×	348,582×	22,639,105×	17,380,453×	738,683×	2,638,649×	13,851,132×	-	-	-	-	-	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	566,815,818×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
45	39 cycles	322,377×	893,881×	7,322,643×	22,639,105×	17,380,453×	738,683×	611,654,490×	13,851,132×	-	-	-	157,472,712×	-	-	11,392,037×	42,655,188×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
47	42 cycles	3,443,253×	243,236,043×	1,477,324×	22,639,105×	102,414,423×	738,683×	147,257,367×	13,851,132×	-	-	-	48,746,880×	-	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	622,370,094×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
49	43 cycles	1,434,463×	84,365,083×	97,046,697×	22,639,105×	26,377,351×	738,683×	147,257,367×	13,851,132×	-	-	-	48,746,880×	1,198,562,668×	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
51	44 cycles	1,323,595×	84,327,963×	83,072,720×	22,639,105×	26,377,351×	738,683×	147,257,367×	13,851,132×	-	1,626,635,598×	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
53	50 cycles	1,313,671×	84,327,963×	81,933,656×	136,110,975×	2,151,459,266×	738,683×	147,257,367×	130,438,299×	-	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
55	54 cycles	1,312,475×	156,408,588×	84,468,557×	91,246,628×	227,194,065×	738,683×	147,257,367×	84,669,038×	-	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	2,868,351,411×
57	57 cycles	1,314,235×	346,218,314×	82,658,804×	83,186,622×	227,194,065×	105,229,096×	147,257,367×	84,669,038×	-	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	1,430,756,397×	-	-	-	-	-	-	2,327,649,737×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
59	63 cycles	1,545,539×	127,413,814×	82,658,804×	83,186,622×	227,194,065×	44,043,839×	277,141,666×	84,669,038×	4,904,857,596×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	478,402,692×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
61	64 cycles	1,337,779×	127,201,770×	82,658,804×	83,186,622×	227,194,065×	30,939,344×	254,541,212×	84,669,038×	454,115,519×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	6,325,958,942×	478,402,692×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
63	68 cycles	1,792,811×	127,201,770×	116,120,722×	8,560,691,882×	227,194,065×	30,939,344×	254,541,212×	176,877,738×	454,115,519×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	478,402,692×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
65	95 cycles	1,321,019×	167,434,899×	224,502,323×	3,214,394,598×	227,194,065×	2,243,478,892×	254,541,212×	320,681,396×	454,115,519×	-	-	5,693,558,429×	151,108,959×	-	11,392,037×	-	-	-	-	-	478,402,692×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
67	127 cycles	1,322,995×	164,884,479×	141,142,202×	3,322,478,070×	227,194,065×	11,345,525,805×	254,541,212×	169,118,150×	454,115,519×	-	101,080,651×	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	478,402,692×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
69	130 cycles	1,672,779×	150,305,012×	141,142,202×	3,247,696,946×	227,194,065×	4,203,923,207×	254,541,212×	180,490,111×	4,683,145,004×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	478,402,692×	-	7,262,311,860×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
71	136 cycles	1,355,939×	256,658,239×	388,983,475×	3,247,696,946×	227,194,065×	4,254,744,935×	254,541,212×	174,438,828×	1,322,143,907×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	-	-	-	478,402,692×	-	3,077,298,320×	-	-	-	-	-	-	-	-	-	-	-	-	-	12,194,076,992×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
73	140 cycles	1,352,759×	744,848,198×	235,215,400×	3,247,696,946×	227,194,065×	4,224,786,284×	254,541,212×	174,438,828×	1,322,143,907×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	4,846,351,950×	10,024,342,851×	-	478,402,692×	-	1,790,933,754×	-	-	-	-	-	-	-	-	4,380,756,819×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
75	142 cycles	1,329,323×	359,035,489×	235,215,400×	3,247,696,946×	227,194,065×	4,224,786,284×	254,541,212×	174,438,828×	22,314,192,983×	490,072,885×	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	3,032,901,505×	2,401,237,715×	-	478,402,692×	-	1,790,933,754×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
77	151 cycles	41,691,001×	770,019,867×	235,215,400×	5,763,386,868×	265,371,866×	4,224,786,284×	1,064,896,873×	174,438,828×	2,093,060,461×	-	-	48,746,880×	151,108,959×	-	11,392,037×	-	-	3,032,901,505×	2,401,237,715×	-	478,402,692×	-	1,790,933,754×	1,198,482,763×	-	-	-	-	-	-	-	-	9,632,617,836×	-	-	14,745,819,772×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-