Base 3: 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] [Base 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] [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

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
1	0 cycles	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
3	1 cycle	-	7×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
5	1 cycle	18×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
7	2 cycles	7×	26×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
9	3 cycles	7×	11×	34×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
11	5 cycles	15×	11×	49×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
13	6 cycles	11×	11×	30×	-	50×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
15	7 cycles	11×	11×	30×	-	23×	58×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
17	10 cycles	19×	27×	30×	42×	23×	27×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
19	12 cycles	15×	19×	30×	93×	23×	27×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
21	13 cycles	15×	19×	30×	54×	23×	27×	-	-	82×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
23	16 cycles	23×	19×	54×	54×	23×	85×	-	-	39×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
25	17 cycles	19×	19×	42×	54×	23×	54×	-	-	39×	-	98×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
27	19 cycles	19×	35×	42×	54×	23×	54×	-	-	39×	90×	47×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
29	22 cycles	27×	27×	66×	54×	23×	54×	-	-	121×	43×	47×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
31	23 cycles	23×	27×	54×	54×	23×	54×	-	-	78×	43×	47×	-	-	122×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
33	26 cycles	23×	27×	54×	54×	153×	54×	-	-	78×	43×	47×	-	-	59×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
35	30 cycles	31×	27×	54×	54×	216×	54×	-	-	78×	43×	47×	-	-	59×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
37	33 cycles	27×	43×	78×	54×	149×	54×	-	-	78×	43×	47×	106×	-	59×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
39	34 cycles	27×	35×	66×	54×	149×	54×	-	-	78×	43×	47×	51×	-	59×	-	-	-	154×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
41	37 cycles	35×	35×	66×	54×	149×	102×	-	-	78×	43×	47×	157×	-	59×	-	-	-	75×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
43	39 cycles	31×	35×	66×	54×	149×	78×	-	-	78×	213×	47×	102×	-	59×	-	-	-	75×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
45	42 cycles	31×	35×	66×	54×	149×	78×	178×	-	78×	126×	47×	102×	-	59×	-	-	-	75×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
47	47 cycles	39×	51×	90×	86×	149×	78×	87×	-	78×	126×	47×	208×	-	59×	-	-	-	75×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
49	48 cycles	35×	43×	78×	70×	149×	78×	87×	-	78×	126×	47×	153×	-	59×	-	-	-	75×	-	-	-	-	194×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
51	50 cycles	35×	43×	102×	70×	149×	78×	87×	-	78×	126×	47×	153×	-	59×	-	-	-	75×	-	-	178×	-	95×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
53	55 cycles	43×	43×	90×	134×	149×	78×	87×	138×	78×	126×	47×	153×	-	59×	-	-	-	75×	-	-	87×	-	95×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
55	56 cycles	39×	43×	90×	102×	149×	78×	87×	67×	78×	126×	47×	153×	-	59×	-	-	-	75×	-	-	87×	-	95×	-	-	218×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
57	59 cycles	39×	59×	90×	102×	189×	78×	87×	67×	78×	126×	47×	153×	-	59×	-	-	-	75×	-	170×	87×	-	95×	-	-	107×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
59	63 cycles	47×	51×	90×	102×	169×	78×	87×	67×	304×	126×	47×	153×	-	59×	-	-	-	75×	-	83×	87×	-	95×	-	-	107×	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
61	64 cycles	43×	51×	90×	102×	169×	78×	87×	67×	189×	126×	47×	153×	-	59×	-	-	-	75×	-	83×	87×	-	95×	-	-	107×	-	-	242×	-	-	-	-	-	-	-	-	-	-	-	-
63	65 cycles	43×	51×	90×	102×	169×	78×	87×	67×	189×	126×	47×	153×	-	59×	-	-	-	75×	-	83×	87×	-	95×	-	-	107×	-	-	119×	250×	-	-	-	-	-	-	-	-	-	-	-
65	72 cycles	51×	51×	138×	102×	169×	280×	87×	67×	189×	126×	47×	153×	-	59×	-	-	-	75×	-	83×	87×	-	95×	-	-	107×	-	-	119×	123×	-	-	-	-	-	-	-	-	-	-	-
67	78 cycles	47×	67×	114×	102×	169×	427×	87×	67×	189×	126×	47×	153×	-	59×	-	-	-	75×	-	83×	87×	-	95×	-	-	107×	-	-	119×	123×	-	-	-	-	-	-	-	-	-	-	-
69	79 cycles	47×	59×	114×	102×	169×	300×	87×	67×	189×	126×	47×	153×	-	59×	-	-	-	75×	-	83×	87×	-	95×	-	-	107×	-	-	119×	123×	-	-	274×	-	-	-	-	-	-	-	-
71	82 cycles	55×	59×	114×	102×	169×	300×	87×	67×	189×	126×	135×	153×	-	59×	-	-	-	75×	-	83×	87×	186×	95×	-	-	107×	-	-	119×	123×	-	-	135×	-	-	-	-	-	-	-	-
73	83 cycles	51×	59×	114×	102×	169×	300×	87×	67×	189×	126×	91×	153×	-	59×	-	-	-	75×	-	83×	87×	91×	95×	-	-	107×	-	-	119×	123×	-	-	135×	-	290×	-	-	-	-	-	-
75	87 cycles	51×	59×	114×	102×	169×	300×	87×	67×	487×	126×	91×	153×	-	59×	-	-	-	75×	-	83×	87×	91×	95×	-	-	107×	-	-	119×	123×	-	-	135×	-	143×	-	-	-	-	-	-
77	92 cycles	59×	75×	114×	134×	169×	300×	87×	67×	336×	206×	91×	153×	-	59×	-	-	-	75×	-	253×	87×	91×	95×	-	-	107×	-	-	119×	123×	-	-	135×	-	143×	-	-	-	-	-	-
79	95 cycles	55×	67×	138×	118×	209×	300×	87×	67×	336×	166×	91×	153×	-	59×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	-	-	119×	373×	-	-	135×	-	143×	-	-	-	-	-	-
81	96 cycles	55×	67×	126×	118×	189×	300×	87×	67×	336×	166×	91×	153×	-	59×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	-	-	119×	246×	-	-	135×	-	143×	-	-	-	322×	-	-
83	100 cycles	63×	67×	150×	118×	189×	300×	87×	67×	408×	166×	91×	153×	-	59×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	226×	-	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	-
85	101 cycles	59×	67×	138×	118×	189×	300×	87×	67×	372×	166×	91×	153×	-	59×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	-	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	338×
87	108 cycles	59×	83×	138×	182×	189×	300×	87×	333×	372×	166×	91×	153×	-	59×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	-	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	167×
89	111 cycles	67×	75×	138×	150×	189×	300×	87×	198×	372×	166×	91×	153×	-	171×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	234×	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	167×
91	115 cycles	63×	75×	138×	150×	189×	300×	87×	198×	372×	166×	453×	153×	-	115×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	115×	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	167×
93	120 cycles	63×	75×	162×	150×	189×	348×	87×	198×	372×	166×	270×	451×	-	115×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	115×	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	167×
95	127 cycles	71×	75×	150×	150×	309×	324×	87×	198×	372×	416×	270×	300×	-	115×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	115×	119×	246×	-	-	135×	-	143×	-	-	-	159×	-	167×
97	130 cycles	67×	91×	150×	150×	249×	324×	87×	198×	444×	289×	270×	300×	-	115×	-	-	-	75×	-	166×	87×	91×	95×	-	-	107×	111×	115×	119×	246×	-	-	135×	-	143×	298×	-	-	159×	-	167×
99	132 cycles	67×	83×	150×	150×	249×	324×	87×	198×	408×	289×	270×	300×	-	115×	-	-	-	75×	-	166×	87×	91×	95×	394×	-	107×	111×	115×	119×	246×	-	-	135×	-	143×	147×	-	-	159×	-	167×