Base 8: Summary: Even Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets]
[Odd Digit Sets]
[Even 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]
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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