Base 2: Maximum Iteration Sequences: Cycle Start

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] — [Base 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] [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]
[Full Cycle]
Cycles Sequences
[Maximum Length Cycle Count]
[All Cycle Counts]

Radix Character Encoding
0	1

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	Max Steps	Max Step Example Cycle Start
1	1 max steps	1 → 0
2	1 max steps	11 → 00
3	1 max steps	100 → 011
4	1 max steps	1000 → 0111
5	1 max steps	10000 → 01111
6	1 max steps	100000 → 011111
7	1 max steps	1000000 → 0111111
8	1 max steps	10000000 → 01111111
9	1 max steps	100000000 → 011111111
10	1 max steps	1000000000 → 0111111111
11	1 max steps	10000000000 → 01111111111
12	1 max steps	100000000000 → 011111111111
13	1 max steps	1000000000000 → 0111111111111
14	1 max steps	10000000000000 → 01111111111111
15	1 max steps	100000000000000 → 011111111111111
16	1 max steps	1000000000000000 → 0111111111111111
17	1 max steps	10000000000000000 → 01111111111111111
18	1 max steps	100000000000000000 → 011111111111111111
19	1 max steps	1000000000000000000 → 0111111111111111111
20	1 max steps	10000000000000000000 → 01111111111111111111
21	1 max steps	100000000000000000000 → 011111111111111111111
22	1 max steps	1000000000000000000000 → 0111111111111111111111
23	1 max steps	10000000000000000000000 → 01111111111111111111111
24	1 max steps	100000000000000000000000 → 011111111111111111111111
25	1 max steps	1000000000000000000000000 → 0111111111111111111111111
26	1 max steps	10000000000000000000000000 → 01111111111111111111111111
27	1 max steps	100000000000000000000000000 → 011111111111111111111111111
28	1 max steps	1000000000000000000000000000 → 0111111111111111111111111111
29	1 max steps	10000000000000000000000000000 → 01111111111111111111111111111
30	1 max steps	100000000000000000000000000000 → 011111111111111111111111111111
31	1 max steps	1000000000000000000000000000000 → 0111111111111111111111111111111
32	1 max steps	10000000000000000000000000000000 → 01111111111111111111111111111111
33	1 max steps	100000000000000000000000000000000 → 011111111111111111111111111111111
34	1 max steps	1000000000000000000000000000000000 → 0111111111111111111111111111111111
35	1 max steps	10000000000000000000000000000000000 → 01111111111111111111111111111111111
36	1 max steps	100000000000000000000000000000000000 → 011111111111111111111111111111111111
37	1 max steps	1000000000000000000000000000000000000 → 0111111111111111111111111111111111111
38	1 max steps	10000000000000000000000000000000000000 → 01111111111111111111111111111111111111
39	1 max steps	100000000000000000000000000000000000000 → 011111111111111111111111111111111111111
40	1 max steps	1000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111
41	1 max steps	10000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111
42	1 max steps	100000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111
43	1 max steps	1000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111
44	1 max steps	10000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111
45	1 max steps	100000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111
46	1 max steps	1000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111
47	1 max steps	10000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111
48	1 max steps	100000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111
49	1 max steps	1000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111
50	1 max steps	10000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111
51	1 max steps	100000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111
52	1 max steps	1000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111
53	1 max steps	10000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111
54	1 max steps	100000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111
55	1 max steps	1000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111
56	1 max steps	10000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111
57	1 max steps	100000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111
58	1 max steps	1000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111
59	1 max steps	10000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111
60	1 max steps	100000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111
61	1 max steps	1000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111
62	1 max steps	10000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111
63	1 max steps	100000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111
64	1 max steps	1000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111
65	1 max steps	10000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111
66	1 max steps	100000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111
67	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111
68	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111
69	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111
70	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111
71	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111
72	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111
73	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111
74	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111
75	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111
76	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111
77	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111
78	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111
79	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111
80	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111
81	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111
82	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111
83	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111111
84	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111111
85	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111111
86	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111111111
87	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111111111
88	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
89	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
90	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
91	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
92	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
93	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
94	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
95	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
96	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
97	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
98	1 max steps	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 01111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
99	1 max steps	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
100	1 max steps	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 → 0111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111