Base 8: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [2] [3] [4] [5] [6] [7] [Base 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]
[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]
[All Cycle Counts]

Radix Character Encoding
0	1	2	3	4	5	6	7

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	# Start Numbers	# Fixed Points (excluding zero)	# Cycles (including fixed) (excluding zero)	Full Cycle Max Length	Avg Steps including Cycle Start	Max Steps including Cycle Start	Avg Steps including Full Cycle	Max Steps including Full Cycle	# Final Numbers (excluding zero)
1	8	0 fixed pts	0 cycles	0 nodes	0.88 avg steps	1 max steps	1.88 avg steps	2 max steps	0 final numbers
2	36	1 fixed pt	2 cycles	3 nodes	1.25 avg steps	2 max steps	3.42 avg steps	5 max steps	4 final numbers
3	120	1 fixed pt	1 cycle	1 node	2.83 avg steps	5 max steps	3.83 avg steps	6 max steps	1 final number
4	330	0 fixed pts	2 cycles	5 nodes	2.28 avg steps	5 max steps	6.62 avg steps	10 max steps	8 final numbers
5	792	0 fixed pts	2 cycles	4 nodes	3.41 avg steps	8 max steps	7.20 avg steps	12 max steps	6 final numbers
6	1,716	2 fixed pts	3 cycles	3 nodes	8.17 avg steps	16 max steps	9.45 avg steps	17 max steps	5 final numbers
7	3,432	1 fixed pt	3 cycles	7 nodes	3.63 avg steps	9 max steps	9.74 avg steps	16 max steps	12 final numbers
8	6,435	1 fixed pt	3 cycles	3 nodes	6.53 avg steps	15 max steps	9.43 avg steps	18 max steps	7 final numbers
9	11,440	1 fixed pt	4 cycles	5 nodes	6.15 avg steps	15 max steps	10.43 avg steps	19 max steps	15 final numbers
10	19,448	1 fixed pt	5 cycles	3 nodes	5.30 avg steps	16 max steps	8.29 avg steps	19 max steps	13 final numbers
11	31,824	0 fixed pts	3 cycles	6 nodes	4.75 avg steps	13 max steps	8.99 avg steps	17 max steps	12 final numbers
12	50,388	4 fixed pts	13 cycles	4 nodes	4.40 avg steps	13 max steps	7.18 avg steps	16 max steps	31 final numbers
13	77,520	0 fixed pts	2 cycles	9 nodes	4.67 avg steps	13 max steps	12.79 avg steps	22 max steps	14 final numbers
14	116,280	4 fixed pts	16 cycles	3 nodes	4.37 avg steps	14 max steps	7.17 avg steps	17 max steps	40 final numbers
15	170,544	2 fixed pts	3 cycles	12 nodes	5.36 avg steps	15 max steps	14.09 avg steps	25 max steps	14 final numbers
16	245,157	2 fixed pts	21 cycles	3 nodes	4.70 avg steps	14 max steps	7.68 avg steps	17 max steps	59 final numbers
17	346,104	2 fixed pts	5 cycles	5 nodes	6.92 avg steps	18 max steps	10.32 avg steps	21 max steps	12 final numbers
18	480,700	4 fixed pts	34 cycles	6 nodes	4.02 avg steps	14 max steps	7.30 avg steps	17 max steps	96 final numbers
19	657,800	2 fixed pts	5 cycles	3 nodes	7.46 avg steps	19 max steps	10.43 avg steps	22 max steps	11 final numbers
20	888,030	3 fixed pts	45 cycles	9 nodes	3.85 avg steps	13 max steps	8.43 avg steps	19 max steps	137 final numbers
21	1,184,040	6 fixed pts	12 cycles	3 nodes	6.15 avg steps	19 max steps	8.77 avg steps	20 max steps	24 final numbers
22	1,560,780	5 fixed pts	62 cycles	12 nodes	4.17 avg steps	15 max steps	9.47 avg steps	23 max steps	184 final numbers
23	2,035,800	2 fixed pts	13 cycles	3 nodes	5.84 avg steps	18 max steps	8.83 avg steps	21 max steps	35 final numbers
24	2,629,575	7 fixed pts	82 cycles	5 nodes	4.96 avg steps	18 max steps	8.12 avg steps	21 max steps	234 final numbers
25	3,365,856	2 fixed pts	22 cycles	6 nodes	5.12 avg steps	18 max steps	8.29 avg steps	21 max steps	64 final numbers
26	4,272,048	6 fixed pts	104 cycles	3 nodes	5.35 avg steps	17 max steps	8.31 avg steps	20 max steps	300 final numbers
27	5,379,616	5 fixed pts	35 cycles	9 nodes	4.68 avg steps	17 max steps	8.45 avg steps	20 max steps	102 final numbers
28	6,724,520	10 fixed pts	137 cycles	3 nodes	4.91 avg steps	16 max steps	7.68 avg steps	17 max steps	391 final numbers
29	8,347,680	5 fixed pts	45 cycles	12 nodes	4.73 avg steps	17 max steps	9.06 avg steps	28 max steps	134 final numbers
30	10,295,472	8 fixed pts	170 cycles	3 nodes	4.81 avg steps	18 max steps	7.79 avg steps	21 max steps	494 final numbers
31	12,620,256	5 fixed pts	61 cycles	5 nodes	5.01 avg steps	19 max steps	8.10 avg steps	22 max steps	175 final numbers
32	15,380,937	8 fixed pts	215 cycles	6 nodes	4.42 avg steps	17 max steps	7.53 avg steps	20 max steps	630 final numbers
33	18,643,560	7 fixed pts	82 cycles	3 nodes	5.18 avg steps	19 max steps	8.14 avg steps	22 max steps	232 final numbers
34	22,481,940	9 fixed pts	264 cycles	9 nodes	4.23 avg steps	16 max steps	7.67 avg steps	22 max steps	782 final numbers
35	26,978,328	11 fixed pts	111 cycles	3 nodes	4.82 avg steps	17 max steps	7.70 avg steps	20 max steps	311 final numbers
36	32,224,114	12 fixed pts	323 cycles	12 nodes	4.31 avg steps	17 max steps	8.11 avg steps	27 max steps	954 final numbers
37	38,320,568	7 fixed pts	139 cycles	3 nodes	4.70 avg steps	18 max steps	7.69 avg steps	21 max steps	402 final numbers
38	45,379,620	11 fixed pts	389 cycles	5 nodes	4.51 avg steps	21 max steps	7.57 avg steps	24 max steps	1,147 final numbers
39	53,524,680	9 fixed pts	179 cycles	6 nodes	4.42 avg steps	18 max steps	7.49 avg steps	22 max steps	521 final numbers
40	62,891,499	12 fixed pts	466 cycles	3 nodes	4.63 avg steps	17 max steps	7.60 avg steps	20 max steps	1,374 final numbers
41	73,629,072	9 fixed pts	223 cycles	9 nodes	4.29 avg steps	17 max steps	7.60 avg steps	23 max steps	659 final numbers
42	85,900,584	21 fixed pts	564 cycles	3 nodes	4.42 avg steps	18 max steps	7.33 avg steps	20 max steps	1,649 final numbers
43	99,884,400	10 fixed pts	275 cycles	12 nodes	4.31 avg steps	17 max steps	7.87 avg steps	29 max steps	814 final numbers
44	115,775,100	14 fixed pts	657 cycles	3 nodes	4.36 avg steps	19 max steps	7.34 avg steps	22 max steps	1,943 final numbers
45	133,784,560	12 fixed pts	338 cycles	5 nodes	4.44 avg steps	22 max steps	7.48 avg steps	25 max steps	992 final numbers
46	154,143,080	15 fixed pts	774 cycles	6 nodes	4.17 avg steps	18 max steps	7.23 avg steps	21 max steps	2,294 final numbers
47	177,100,560	13 fixed pts	410 cycles	3 nodes	4.48 avg steps	18 max steps	7.47 avg steps	21 max steps	1,203 final numbers
48	202,927,725	18 fixed pts	905 cycles	9 nodes	4.08 avg steps	17 max steps	7.31 avg steps	24 max steps	2,687 final numbers
49	231,917,400	20 fixed pts	498 cycles	3 nodes	4.35 avg steps	18 max steps	7.28 avg steps	21 max steps	1,454 final numbers
50	264,385,836	18 fixed pts	1,048 cycles	12 nodes	4.10 avg steps	17 max steps	7.51 avg steps	28 max steps	3,117 final numbers
51	300,674,088	15 fixed pts	587 cycles	3 nodes	4.29 avg steps	19 max steps	7.28 avg steps	22 max steps	1,731 final numbers
52	341,149,446	20 fixed pts	1,212 cycles	5 nodes	4.20 avg steps	23 max steps	7.23 avg steps	26 max steps	3,597 final numbers
53	386,206,920	15 fixed pts	696 cycles	6 nodes	4.13 avg steps	17 max steps	7.18 avg steps	22 max steps	2,060 final numbers
54	436,270,780	23 fixed pts	1,392 cycles	3 nodes	4.25 avg steps	19 max steps	7.23 avg steps	22 max steps	4,130 final numbers
55	491,796,152	16 fixed pts	818 cycles	9 nodes	4.05 avg steps	17 max steps	7.24 avg steps	25 max steps	2,430 final numbers
56	553,270,671	30 fixed pts	1,598 cycles	3 nodes	4.15 avg steps	18 max steps	7.10 avg steps	21 max steps	4,734 final numbers
57	621,216,192	20 fixed pts	958 cycles	12 nodes	4.07 avg steps	17 max steps	7.39 avg steps	29 max steps	2,842 final numbers
58	696,190,560	23 fixed pts	1,811 cycles	3 nodes	4.11 avg steps	20 max steps	7.10 avg steps	23 max steps	5,387 final numbers
59	778,789,440	20 fixed pts	1,110 cycles	5 nodes	4.15 avg steps	24 max steps	7.17 avg steps	27 max steps	3,292 final numbers
60	869,648,208	26 fixed pts	2,058 cycles	6 nodes	3.99 avg steps	19 max steps	7.03 avg steps	22 max steps	6,124 final numbers
61	969,443,904	21 fixed pts	1,281 cycles	3 nodes	4.17 avg steps	19 max steps	7.16 avg steps	22 max steps	3,801 final numbers
62	1,078,897,248	27 fixed pts	2,326 cycles	9 nodes	3.94 avg steps	19 max steps	7.09 avg steps	26 max steps	6,931 final numbers
63	1,198,774,720	32 fixed pts	1,482 cycles	3 nodes	4.09 avg steps	21 max steps	7.05 avg steps	24 max steps	4,382 final numbers
64	1,329,890,705	29 fixed pts	2,617 cycles	12 nodes	3.96 avg steps	19 max steps	7.21 avg steps	30 max steps	7,802 final numbers
65	1,473,109,704	23 fixed pts	1,684 cycles	3 nodes	4.06 avg steps	21 max steps	7.05 avg steps	24 max steps	5,006 final numbers
66	1,629,348,612	32 fixed pts	2,938 cycles	5 nodes	4.03 avg steps	25 max steps	7.05 avg steps	28 max steps	8,752 final numbers
67	1,799,579,064	25 fixed pts	1,922 cycles	6 nodes	3.95 avg steps	19 max steps	6.99 avg steps	22 max steps	5,717 final numbers
68	1,984,829,850	32 fixed pts	3,284 cycles	3 nodes	4.05 avg steps	22 max steps	7.04 avg steps	25 max steps	9,788 final numbers
69	2,186,189,400	28 fixed pts	2,180 cycles	9 nodes	3.92 avg steps	19 max steps	7.04 avg steps	27 max steps	6,492 final numbers
70	2,404,808,340	43 fixed pts	3,672 cycles	3 nodes	3.99 avg steps	19 max steps	6.96 avg steps	22 max steps	10,930 final numbers
71	2,641,902,120	29 fixed pts	2,461 cycles	12 nodes	3.93 avg steps	19 max steps	7.13 avg steps	30 max steps	7,334 final numbers
72	2,898,753,715	37 fixed pts	4,076 cycles	3 nodes	3.97 avg steps	21 max steps	6.96 avg steps	24 max steps	12,153 final numbers
73	3,176,716,400	30 fixed pts	2,770 cycles	5 nodes	3.99 avg steps	25 max steps	7.00 avg steps	28 max steps	8,252 final numbers
74	3,477,216,600	37 fixed pts	4,520 cycles	6 nodes	3.88 avg steps	21 max steps	6.91 avg steps	27 max steps	13,488 final numbers
75	3,801,756,816	33 fixed pts	3,108 cycles	3 nodes	3.99 avg steps	21 max steps	6.99 avg steps	24 max steps	9,258 final numbers
76	4,151,918,628	39 fixed pts	5,000 cycles	9 nodes	3.85 avg steps	19 max steps	6.95 avg steps	26 max steps	14,930 final numbers
77	4,529,365,776	45 fixed pts	3,487 cycles	3 nodes	3.95 avg steps	21 max steps	6.92 avg steps	24 max steps	10,370 final numbers
78	4,935,847,320	43 fixed pts	5,518 cycles	12 nodes	3.86 avg steps	19 max steps	7.03 avg steps	30 max steps	16,477 final numbers
79	5,373,200,880	35 fixed pts	3,874 cycles	3 nodes	3.92 avg steps	23 max steps	6.92 avg steps	26 max steps	11,552 final numbers
80	5,843,355,957	43 fixed pts	6,073 cycles	5 nodes	3.91 avg steps	25 max steps	6.92 avg steps	28 max steps	18,135 final numbers
81	6,348,337,336	38 fixed pts	4,310 cycles	6 nodes	3.84 avg steps	20 max steps	6.87 avg steps	24 max steps	12,856 final numbers
82	6,890,268,572	46 fixed pts	6,672 cycles	3 nodes	3.92 avg steps	21 max steps	6.91 avg steps	24 max steps	19,923 final numbers
83	7,471,375,560	39 fixed pts	4,777 cycles	9 nodes	3.82 avg steps	20 max steps	6.91 avg steps	29 max steps	14,261 final numbers
84	8,093,990,190	61 fixed pts	7,325 cycles	3 nodes	3.88 avg steps	24 max steps	6.86 avg steps	27 max steps	21,853 final numbers
85	8,760,554,088	41 fixed pts	5,281 cycles	12 nodes	3.83 avg steps	21 max steps	6.97 avg steps	33 max steps	15,770 final numbers
86	9,473,622,444	49 fixed pts	7,998 cycles	3 nodes	3.87 avg steps	22 max steps	6.86 avg steps	25 max steps	23,896 final numbers
87	10,235,867,928	45 fixed pts	5,828 cycles	5 nodes	3.87 avg steps	28 max steps	6.89 avg steps	31 max steps	17,395 final numbers
88	11,050,084,695	51 fixed pts	8,734 cycles	6 nodes	3.80 avg steps	20 max steps	6.82 avg steps	26 max steps	26,102 final numbers
89	11,919,192,480	46 fixed pts	6,410 cycles	3 nodes	3.88 avg steps	23 max steps	6.87 avg steps	26 max steps	19,138 final numbers
90	12,846,240,784	55 fixed pts	9,519 cycles	9 nodes	3.78 avg steps	20 max steps	6.86 avg steps	29 max steps	28,455 final numbers
91	13,834,413,152	60 fixed pts	7,050 cycles	3 nodes	3.85 avg steps	22 max steps	6.83 avg steps	25 max steps	21,030 final numbers
92	14,887,031,544	57 fixed pts	10,354 cycles	12 nodes	3.79 avg steps	21 max steps	6.91 avg steps	33 max steps	30,956 final numbers
93	16,007,560,800	50 fixed pts	7,711 cycles	3 nodes	3.83 avg steps	25 max steps	6.83 avg steps	28 max steps	23,033 final numbers
94	17,199,613,200	59 fixed pts	11,242 cycles	5 nodes	3.83 avg steps	28 max steps	6.84 avg steps	31 max steps	33,610 final numbers
95	18,466,953,120	51 fixed pts	8,432 cycles	6 nodes	3.77 avg steps	21 max steps	6.80 avg steps	27 max steps	25,196 final numbers
96	19,813,501,785	63 fixed pts	12,188 cycles	3 nodes	3.83 avg steps	23 max steps	6.83 avg steps	26 max steps	36,438 final numbers
97	21,243,342,120	54 fixed pts	9,203 cycles	9 nodes	3.75 avg steps	21 max steps	6.83 avg steps	30 max steps	27,508 final numbers
98	22,760,723,700	77 fixed pts	13,204 cycles	3 nodes	3.81 avg steps	24 max steps	6.79 avg steps	27 max steps	39,458 final numbers
99	24,370,067,800	58 fixed pts	10,023 cycles	12 nodes	3.76 avg steps	23 max steps	6.87 avg steps	34 max steps	29,962 final numbers
100	26,075,972,546	65 fixed pts	14,255 cycles	3 nodes	3.80 avg steps	24 max steps	6.79 avg steps	27 max steps	42,635 final numbers