Base 6: Cycles Sequences: Maximum Length Cycle Count

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]
Iteration Frequencies
[Cycle Start]
[Full Cycle]
Maximum Iteration Sequences
[Cycle Start]
[Full Cycle]
Cycles Sequences
[Maximum Length Cycle Count] — [2] [3] [4] [5] [Base 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]
[All Cycle Counts]

Radix Character Encoding
0	1	2	3	4	5

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)	Max Cycle Length	Longest Full Cycles (excluding zero) (bold = exactly one cycle [excluding zero])
1	0 cycles	-	-
2	1 cycle	3 nodes	⮎ 05 → 41 → 23 ⮌
3	1 cycle	(fixed) 1 node	⮎ 253 ⮌
4	1 cycle	6 nodes	⮎ 1554 → 4042 → 4132 → 3043 → 3552 → 3133 ⮌
5	2 cycles	2 nodes	⮎ 31533 → 35552 ⮌
6	4 cycles	3 nodes	⮎ 205544 → 525521 → 432222 ⮌
7	1 cycle	2 nodes	⮎ 4405412 → 5315321 ⮌
8	5 cycles	7 nodes	⮎ 31104443 → 43255222 → 33204323 → 41055442 → 54155311 → 44404112 → 43313222 ⮌
9	2 cycles	2 nodes	⮎ 441054412 → 533153221 ⮌
10	7 cycles	2 nodes	⮎ 5531044201 → 5533042201 ⮌
11	3 cycles	2 nodes	⮎ 44110544412 → 53331532221 ⮌
12	9 cycles	2 nodes	⮎ 555310442001 → 555330422001 ⮌
13	4 cycles	2 nodes	⮎ 5432105443211 → 5433205432211 ⮌
14	13 cycles	2 nodes	⮎ 55553104420001 → 55553304220001 ⮌
15	7 cycles	2 nodes	⮎ 554321054432101 → 554332054322101 ⮌
16	17 cycles	2 nodes	⮎ 5555531044200001 → 5555533042200001 ⮌
17	8 cycles	2 nodes	⮎ 55543210544321001 → 55543320543221001 ⮌
18	24 cycles	2 nodes	⮎ 555555310442000001 → 555555330422000001 ⮌
19	11 cycles	2 nodes	⮎ 5555432105443210001 → 5555433205432210001 ⮌
20	30 cycles	2 nodes	⮎ 55555553104420000001 → 55555553304220000001 ⮌
21	16 cycles	2 nodes	⮎ 555554321054432100001 → 555554332054322100001 ⮌
22	37 cycles	2 nodes	⮎ 5555555531044200000001 → 5555555533042200000001 ⮌
23	21 cycles	2 nodes	⮎ 55555543210544321000001 → 55555543320543221000001 ⮌
24	46 cycles	2 nodes	⮎ 555555555310442000000001 → 555555555330422000000001 ⮌
25	27 cycles	2 nodes	⮎ 5555555432105443210000001 → 5555555433205432210000001 ⮌
26	57 cycles	2 nodes	⮎ 55555555553104420000000001 → 55555555553304220000000001 ⮌
27	34 cycles	2 nodes	⮎ 555555554321054432100000001 → 555555554332054322100000001 ⮌
28	68 cycles	2 nodes	⮎ 5555555555531044200000000001 → 5555555555533042200000000001 ⮌
29	42 cycles	2 nodes	⮎ 55555555543210544321000000001 → 55555555543320543221000000001 ⮌
30	83 cycles	2 nodes	⮎ 555555555555310442000000000001 → 555555555555330422000000000001 ⮌
31	52 cycles	2 nodes	⮎ 5555555555432105443210000000001 → 5555555555433205432210000000001 ⮌
32	96 cycles	2 nodes	⮎ 55555555555553104420000000000001 → 55555555555553304220000000000001 ⮌
33	64 cycles	2 nodes	⮎ 555555555554321054432100000000001 → 555555555554332054322100000000001 ⮌
34	113 cycles	2 nodes	⮎ 5555555555555531044200000000000001 → 5555555555555533042200000000000001 ⮌
35	77 cycles	2 nodes	⮎ 55555555555543210544321000000000001 → 55555555555543320543221000000000001 ⮌
36	132 cycles	2 nodes	⮎ 555555555555555310442000000000000001 → 555555555555555330422000000000000001 ⮌
37	90 cycles	2 nodes	⮎ 5555555555555432105443210000000000001 → 5555555555555433205432210000000000001 ⮌
38	153 cycles	2 nodes	⮎ 55555555555555553104420000000000000001 → 55555555555555553304220000000000000001 ⮌
39	107 cycles	2 nodes	⮎ 555555555555554321054432100000000000001 → 555555555555554332054322100000000000001 ⮌
40	175 cycles	2 nodes	⮎ 5555555555555555531044200000000000000001 → 5555555555555555533042200000000000000001 ⮌
41	125 cycles	2 nodes	⮎ 55555555555555543210544321000000000000001 → 55555555555555543320543221000000000000001 ⮌
42	200 cycles	2 nodes	⮎ 555555555555555555310442000000000000000001 → 555555555555555555330422000000000000000001 ⮌
43	145 cycles	2 nodes	⮎ 5555555555555555432105443210000000000000001 → 5555555555555555433205432210000000000000001 ⮌
44	226 cycles	2 nodes	⮎ 55555555555555555553104420000000000000000001 → 55555555555555555553304220000000000000000001 ⮌
45	168 cycles	2 nodes	⮎ 555555555555555554321054432100000000000000001 → 555555555555555554332054322100000000000000001 ⮌
46	256 cycles	2 nodes	⮎ 5555555555555555555531044200000000000000000001 → 5555555555555555555533042200000000000000000001 ⮌
47	191 cycles	2 nodes	⮎ 55555555555555555543210544321000000000000000001 → 55555555555555555543320543221000000000000000001 ⮌
48	288 cycles	2 nodes	⮎ 555555555555555555555310442000000000000000000001 → 555555555555555555555330422000000000000000000001 ⮌
49	217 cycles	2 nodes	⮎ 5555555555555555555432105443210000000000000000001 → 5555555555555555555433205432210000000000000000001 ⮌
50	323 cycles	2 nodes	⮎ 55555555555555555555553104420000000000000000000001 → 55555555555555555555553304220000000000000000000001 ⮌
51	247 cycles	2 nodes	⮎ 555555555555555555554321054432100000000000000000001 → 555555555555555555554332054322100000000000000000001 ⮌
52	358 cycles	2 nodes	⮎ 5555555555555555555555531044200000000000000000000001 → 5555555555555555555555533042200000000000000000000001 ⮌
53	278 cycles	2 nodes	⮎ 55555555555555555555543210544321000000000000000000001 → 55555555555555555555543320543221000000000000000000001 ⮌
54	399 cycles	2 nodes	⮎ 555555555555555555555555310442000000000000000000000001 → 555555555555555555555555330422000000000000000000000001 ⮌
55	312 cycles	2 nodes	⮎ 5555555555555555555555432105443210000000000000000000001 → 5555555555555555555555433205432210000000000000000000001 ⮌
56	441 cycles	2 nodes	⮎ 55555555555555555555555553104420000000000000000000000001 → 55555555555555555555555553304220000000000000000000000001 ⮌
57	348 cycles	2 nodes	⮎ 555555555555555555555554321054432100000000000000000000001 → 555555555555555555555554332054322100000000000000000000001 ⮌
58	487 cycles	2 nodes	⮎ 5555555555555555555555555531044200000000000000000000000001 → 5555555555555555555555555533042200000000000000000000000001 ⮌
59	387 cycles	2 nodes	⮎ 55555555555555555555555543210544321000000000000000000000001 → 55555555555555555555555543320543221000000000000000000000001 ⮌
60	536 cycles	2 nodes	⮎ 555555555555555555555555555310442000000000000000000000000001 → 555555555555555555555555555330422000000000000000000000000001 ⮌
61	429 cycles	2 nodes	⮎ 5555555555555555555555555432105443210000000000000000000000001 → 5555555555555555555555555433205432210000000000000000000000001 ⮌
62	587 cycles	2 nodes	⮎ 55555555555555555555555555553104420000000000000000000000000001 → 55555555555555555555555555553304220000000000000000000000000001 ⮌
63	475 cycles	2 nodes	⮎ 555555555555555555555555554321054432100000000000000000000000001 → 555555555555555555555555554332054322100000000000000000000000001 ⮌
64	641 cycles	2 nodes	⮎ 5555555555555555555555555555531044200000000000000000000000000001 → 5555555555555555555555555555533042200000000000000000000000000001 ⮌
65	523 cycles	2 nodes	⮎ 55555555555555555555555555543210544321000000000000000000000000001 → 55555555555555555555555555543320543221000000000000000000000000001 ⮌
66	701 cycles	2 nodes	⮎ 555555555555555555555555555555310442000000000000000000000000000001 → 555555555555555555555555555555330422000000000000000000000000000001 ⮌
67	573 cycles	2 nodes	⮎ 5555555555555555555555555555432105443210000000000000000000000000001 → 5555555555555555555555555555433205432210000000000000000000000000001 ⮌
68	762 cycles	2 nodes	⮎ 55555555555555555555555555555553104420000000000000000000000000000001 → 55555555555555555555555555555553304220000000000000000000000000000001 ⮌
69	628 cycles	2 nodes	⮎ 555555555555555555555555555554321054432100000000000000000000000000001 → 555555555555555555555555555554332054322100000000000000000000000000001 ⮌
70	828 cycles	2 nodes	⮎ 5555555555555555555555555555555531044200000000000000000000000000000001 → 5555555555555555555555555555555533042200000000000000000000000000000001 ⮌
71	686 cycles	2 nodes	⮎ 55555555555555555555555555555543210544321000000000000000000000000000001 → 55555555555555555555555555555543320543221000000000000000000000000000001 ⮌
72	896 cycles	2 nodes	⮎ 555555555555555555555555555555555310442000000000000000000000000000000001 → 555555555555555555555555555555555330422000000000000000000000000000000001 ⮌
73	747 cycles	2 nodes	⮎ 5555555555555555555555555555555432105443210000000000000000000000000000001 → 5555555555555555555555555555555433205432210000000000000000000000000000001 ⮌
74	969 cycles	2 nodes	⮎ 55555555555555555555555555555555553104420000000000000000000000000000000001 → 55555555555555555555555555555555553304220000000000000000000000000000000001 ⮌
75	813 cycles	2 nodes	⮎ 555555555555555555555555555555554321054432100000000000000000000000000000001 → 555555555555555555555555555555554332054322100000000000000000000000000000001 ⮌
76	1,045 cycles	2 nodes	⮎ 5555555555555555555555555555555555531044200000000000000000000000000000000001 → 5555555555555555555555555555555555533042200000000000000000000000000000000001 ⮌
77	880 cycles	2 nodes	⮎ 55555555555555555555555555555555543210544321000000000000000000000000000000001 → 55555555555555555555555555555555543320543221000000000000000000000000000000001 ⮌
78	1,127 cycles	2 nodes	⮎ 555555555555555555555555555555555555310442000000000000000000000000000000000001 → 555555555555555555555555555555555555330422000000000000000000000000000000000001 ⮌
79	952 cycles	2 nodes	⮎ 5555555555555555555555555555555555432105443210000000000000000000000000000000001 → 5555555555555555555555555555555555433205432210000000000000000000000000000000001 ⮌
80	1,211 cycles	2 nodes	⮎ 55555555555555555555555555555555555553104420000000000000000000000000000000000001 → 55555555555555555555555555555555555553304220000000000000000000000000000000000001 ⮌
81	1,029 cycles	2 nodes	⮎ 555555555555555555555555555555555554321054432100000000000000000000000000000000001 → 555555555555555555555555555555555554332054322100000000000000000000000000000000001 ⮌
82	1,299 cycles	2 nodes	⮎ 5555555555555555555555555555555555555531044200000000000000000000000000000000000001 → 5555555555555555555555555555555555555533042200000000000000000000000000000000000001 ⮌
83	1,109 cycles	2 nodes	⮎ 55555555555555555555555555555555555543210544321000000000000000000000000000000000001 → 55555555555555555555555555555555555543320543221000000000000000000000000000000000001 ⮌
84	1,392 cycles	2 nodes	⮎ 555555555555555555555555555555555555555310442000000000000000000000000000000000000001 → 555555555555555555555555555555555555555330422000000000000000000000000000000000000001 ⮌
85	1,193 cycles	2 nodes	⮎ 5555555555555555555555555555555555555432105443210000000000000000000000000000000000001 → 5555555555555555555555555555555555555433205432210000000000000000000000000000000000001 ⮌
86	1,490 cycles	2 nodes	⮎ 55555555555555555555555555555555555555553104420000000000000000000000000000000000000001 → 55555555555555555555555555555555555555553304220000000000000000000000000000000000000001 ⮌
87	1,281 cycles	2 nodes	⮎ 555555555555555555555555555555555555554321054432100000000000000000000000000000000000001 → 555555555555555555555555555555555555554332054322100000000000000000000000000000000000001 ⮌
88	1,591 cycles	2 nodes	⮎ 5555555555555555555555555555555555555555531044200000000000000000000000000000000000000001 → 5555555555555555555555555555555555555555533042200000000000000000000000000000000000000001 ⮌
89	1,373 cycles	2 nodes	⮎ 55555555555555555555555555555555555555543210544321000000000000000000000000000000000000001 → 55555555555555555555555555555555555555543320543221000000000000000000000000000000000000001 ⮌
90	1,699 cycles	2 nodes	⮎ 555555555555555555555555555555555555555555310442000000000000000000000000000000000000000001 → 555555555555555555555555555555555555555555330422000000000000000000000000000000000000000001 ⮌
91	1,470 cycles	2 nodes	⮎ 5555555555555555555555555555555555555555432105443210000000000000000000000000000000000000001 → 5555555555555555555555555555555555555555433205432210000000000000000000000000000000000000001 ⮌
92	1,808 cycles	2 nodes	⮎ 55555555555555555555555555555555555555555553104420000000000000000000000000000000000000000001 → 55555555555555555555555555555555555555555553304220000000000000000000000000000000000000000001 ⮌
93	1,572 cycles	2 nodes	⮎ 555555555555555555555555555555555555555554321054432100000000000000000000000000000000000000001 → 555555555555555555555555555555555555555554332054322100000000000000000000000000000000000000001 ⮌
94	1,924 cycles	2 nodes	⮎ 5555555555555555555555555555555555555555555531044200000000000000000000000000000000000000000001 → 5555555555555555555555555555555555555555555533042200000000000000000000000000000000000000000001 ⮌
95	1,678 cycles	2 nodes	⮎ 55555555555555555555555555555555555555555543210544321000000000000000000000000000000000000000001 → 55555555555555555555555555555555555555555543320543221000000000000000000000000000000000000000001 ⮌
96	2,045 cycles	2 nodes	⮎ 555555555555555555555555555555555555555555555310442000000000000000000000000000000000000000000001 → 555555555555555555555555555555555555555555555330422000000000000000000000000000000000000000000001 ⮌
97	1,787 cycles	2 nodes	⮎ 5555555555555555555555555555555555555555555432105443210000000000000000000000000000000000000000001 → 5555555555555555555555555555555555555555555433205432210000000000000000000000000000000000000000001 ⮌
98	2,171 cycles	2 nodes	⮎ 55555555555555555555555555555555555555555555553104420000000000000000000000000000000000000000000001 → 55555555555555555555555555555555555555555555553304220000000000000000000000000000000000000000000001 ⮌
99	1,903 cycles	2 nodes	⮎ 555555555555555555555555555555555555555555554321054432100000000000000000000000000000000000000000001 → 555555555555555555555555555555555555555555554332054322100000000000000000000000000000000000000000001 ⮌
100	2,301 cycles	2 nodes	⮎ 5555555555555555555555555555555555555555555555531044200000000000000000000000000000000000000000000001 → 5555555555555555555555555555555555555555555555533042200000000000000000000000000000000000000000000001 ⮌