Base 6: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [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]
[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

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	6	0 fixed pts	0 cycles	0 nodes	0.83 avg steps	1 max steps	1.83 avg steps	2 max steps	0 final numbers
2	21	0 fixed pts	1 cycle	3 nodes	1.14 avg steps	2 max steps	3.57 avg steps	5 max steps	3 final numbers
3	56	1 fixed pt	1 cycle	1 node	2.34 avg steps	4 max steps	3.34 avg steps	5 max steps	1 final number
4	126	0 fixed pts	1 cycle	6 nodes	1.75 avg steps	4 max steps	7.52 avg steps	10 max steps	6 final numbers
5	252	1 fixed pt	2 cycles	2 nodes	3.16 avg steps	6 max steps	4.43 avg steps	7 max steps	3 final numbers
6	462	3 fixed pts	4 cycles	3 nodes	3.44 avg steps	7 max steps	5.66 avg steps	10 max steps	6 final numbers
7	792	0 fixed pts	1 cycle	2 nodes	5.86 avg steps	10 max steps	7.85 avg steps	12 max steps	2 final numbers
8	1,287	2 fixed pts	5 cycles	7 nodes	2.81 avg steps	7 max steps	6.98 avg steps	13 max steps	13 final numbers
9	2,002	1 fixed pt	2 cycles	2 nodes	6.72 avg steps	13 max steps	8.71 avg steps	15 max steps	3 final numbers
10	3,003	4 fixed pts	7 cycles	2 nodes	4.64 avg steps	12 max steps	5.94 avg steps	13 max steps	10 final numbers
11	4,368	2 fixed pts	3 cycles	2 nodes	5.58 avg steps	12 max steps	7.37 avg steps	14 max steps	4 final numbers
12	6,188	3 fixed pts	9 cycles	2 nodes	5.21 avg steps	14 max steps	7.18 avg steps	16 max steps	15 final numbers
13	8,568	2 fixed pts	4 cycles	2 nodes	5.45 avg steps	11 max steps	7.41 avg steps	13 max steps	6 final numbers
14	11,628	5 fixed pts	13 cycles	2 nodes	5.42 avg steps	14 max steps	7.28 avg steps	16 max steps	21 final numbers
15	15,504	4 fixed pts	7 cycles	2 nodes	5.07 avg steps	13 max steps	6.84 avg steps	15 max steps	10 final numbers
16	20,349	5 fixed pts	17 cycles	2 nodes	5.20 avg steps	14 max steps	7.05 avg steps	16 max steps	29 final numbers
17	26,334	3 fixed pts	8 cycles	2 nodes	5.27 avg steps	15 max steps	7.23 avg steps	17 max steps	13 final numbers
18	33,649	8 fixed pts	24 cycles	2 nodes	4.95 avg steps	17 max steps	6.86 avg steps	19 max steps	40 final numbers
19	42,504	4 fixed pts	11 cycles	2 nodes	5.39 avg steps	17 max steps	7.24 avg steps	19 max steps	18 final numbers
20	53,130	8 fixed pts	30 cycles	2 nodes	4.73 avg steps	15 max steps	6.56 avg steps	17 max steps	52 final numbers
21	65,780	6 fixed pts	16 cycles	2 nodes	5.39 avg steps	19 max steps	7.28 avg steps	21 max steps	26 final numbers
22	80,730	9 fixed pts	37 cycles	2 nodes	5.01 avg steps	17 max steps	6.93 avg steps	19 max steps	65 final numbers
23	98,280	7 fixed pts	21 cycles	2 nodes	5.13 avg steps	21 max steps	7.04 avg steps	23 max steps	35 final numbers
24	118,755	10 fixed pts	46 cycles	2 nodes	5.14 avg steps	19 max steps	7.05 avg steps	21 max steps	82 final numbers
25	142,506	8 fixed pts	27 cycles	2 nodes	4.98 avg steps	23 max steps	6.87 avg steps	25 max steps	46 final numbers
26	169,911	13 fixed pts	57 cycles	2 nodes	5.10 avg steps	21 max steps	6.99 avg steps	23 max steps	101 final numbers
27	201,376	9 fixed pts	34 cycles	2 nodes	5.12 avg steps	25 max steps	7.05 avg steps	27 max steps	59 final numbers
28	237,336	13 fixed pts	68 cycles	2 nodes	4.95 avg steps	23 max steps	6.87 avg steps	25 max steps	123 final numbers
29	278,256	10 fixed pts	42 cycles	2 nodes	5.17 avg steps	27 max steps	7.10 avg steps	29 max steps	74 final numbers
30	324,632	17 fixed pts	83 cycles	2 nodes	4.86 avg steps	25 max steps	6.77 avg steps	27 max steps	149 final numbers
31	376,992	12 fixed pts	52 cycles	2 nodes	5.16 avg steps	29 max steps	7.06 avg steps	31 max steps	92 final numbers
32	435,897	16 fixed pts	96 cycles	2 nodes	5.02 avg steps	27 max steps	6.96 avg steps	29 max steps	176 final numbers
33	501,942	14 fixed pts	64 cycles	2 nodes	5.10 avg steps	31 max steps	7.04 avg steps	33 max steps	114 final numbers
34	575,757	19 fixed pts	113 cycles	2 nodes	5.11 avg steps	29 max steps	7.04 avg steps	31 max steps	207 final numbers
35	658,008	16 fixed pts	77 cycles	2 nodes	4.97 avg steps	33 max steps	6.89 avg steps	35 max steps	138 final numbers
36	749,398	21 fixed pts	132 cycles	2 nodes	5.11 avg steps	31 max steps	7.03 avg steps	33 max steps	243 final numbers
37	850,668	16 fixed pts	90 cycles	2 nodes	5.11 avg steps	35 max steps	7.06 avg steps	37 max steps	164 final numbers
38	962,598	24 fixed pts	153 cycles	2 nodes	5.08 avg steps	33 max steps	7.01 avg steps	35 max steps	282 final numbers
39	1,086,008	19 fixed pts	107 cycles	2 nodes	5.17 avg steps	37 max steps	7.11 avg steps	39 max steps	195 final numbers
40	1,221,759	25 fixed pts	175 cycles	2 nodes	4.99 avg steps	35 max steps	6.92 avg steps	37 max steps	325 final numbers
41	1,370,754	21 fixed pts	125 cycles	2 nodes	5.19 avg steps	39 max steps	7.12 avg steps	41 max steps	229 final numbers
42	1,533,939	28 fixed pts	200 cycles	2 nodes	5.15 avg steps	37 max steps	7.10 avg steps	39 max steps	372 final numbers
43	1,712,304	23 fixed pts	145 cycles	2 nodes	5.16 avg steps	41 max steps	7.10 avg steps	43 max steps	267 final numbers
44	1,906,884	29 fixed pts	226 cycles	2 nodes	5.21 avg steps	39 max steps	7.15 avg steps	41 max steps	423 final numbers
45	2,118,760	26 fixed pts	168 cycles	2 nodes	5.08 avg steps	43 max steps	7.02 avg steps	45 max steps	310 final numbers
46	2,349,060	33 fixed pts	256 cycles	2 nodes	5.27 avg steps	41 max steps	7.20 avg steps	43 max steps	479 final numbers
47	2,598,960	27 fixed pts	191 cycles	2 nodes	5.20 avg steps	45 max steps	7.15 avg steps	47 max steps	355 final numbers
48	2,869,685	35 fixed pts	288 cycles	2 nodes	5.26 avg steps	43 max steps	7.21 avg steps	45 max steps	541 final numbers
49	3,162,510	29 fixed pts	217 cycles	2 nodes	5.26 avg steps	47 max steps	7.21 avg steps	49 max steps	405 final numbers
50	3,478,761	39 fixed pts	323 cycles	2 nodes	5.20 avg steps	45 max steps	7.14 avg steps	47 max steps	607 final numbers
51	3,819,816	33 fixed pts	247 cycles	2 nodes	5.30 avg steps	49 max steps	7.25 avg steps	51 max steps	461 final numbers
52	4,187,106	39 fixed pts	358 cycles	2 nodes	5.33 avg steps	47 max steps	7.28 avg steps	49 max steps	677 final numbers
53	4,582,116	35 fixed pts	278 cycles	2 nodes	5.31 avg steps	51 max steps	7.26 avg steps	53 max steps	521 final numbers
54	5,006,386	44 fixed pts	399 cycles	2 nodes	5.39 avg steps	49 max steps	7.34 avg steps	51 max steps	754 final numbers
55	5,461,512	38 fixed pts	312 cycles	2 nodes	5.24 avg steps	53 max steps	7.19 avg steps	55 max steps	586 final numbers
56	5,949,147	46 fixed pts	441 cycles	2 nodes	5.44 avg steps	51 max steps	7.39 avg steps	53 max steps	836 final numbers
57	6,471,002	40 fixed pts	348 cycles	2 nodes	5.37 avg steps	55 max steps	7.33 avg steps	57 max steps	656 final numbers
58	7,028,847	50 fixed pts	487 cycles	2 nodes	5.46 avg steps	53 max steps	7.41 avg steps	55 max steps	924 final numbers
59	7,624,512	43 fixed pts	387 cycles	2 nodes	5.42 avg steps	57 max steps	7.38 avg steps	59 max steps	731 final numbers
60	8,259,888	53 fixed pts	536 cycles	2 nodes	5.41 avg steps	55 max steps	7.36 avg steps	57 max steps	1,019 final numbers
61	8,936,928	46 fixed pts	429 cycles	2 nodes	5.48 avg steps	59 max steps	7.43 avg steps	61 max steps	812 final numbers
62	9,657,648	56 fixed pts	587 cycles	2 nodes	5.54 avg steps	57 max steps	7.50 avg steps	59 max steps	1,118 final numbers
63	10,424,128	50 fixed pts	475 cycles	2 nodes	5.49 avg steps	61 max steps	7.45 avg steps	63 max steps	900 final numbers
64	11,238,513	58 fixed pts	641 cycles	2 nodes	5.59 avg steps	59 max steps	7.55 avg steps	61 max steps	1,224 final numbers
65	12,103,014	53 fixed pts	523 cycles	2 nodes	5.44 avg steps	63 max steps	7.40 avg steps	65 max steps	993 final numbers
66	13,019,909	64 fixed pts	701 cycles	2 nodes	5.66 avg steps	61 max steps	7.61 avg steps	63 max steps	1,338 final numbers
67	13,991,544	55 fixed pts	573 cycles	2 nodes	5.56 avg steps	65 max steps	7.53 avg steps	67 max steps	1,091 final numbers
68	15,020,334	66 fixed pts	762 cycles	2 nodes	5.68 avg steps	63 max steps	7.64 avg steps	65 max steps	1,458 final numbers
69	16,108,764	59 fixed pts	628 cycles	2 nodes	5.62 avg steps	67 max steps	7.58 avg steps	69 max steps	1,197 final numbers
70	17,259,390	71 fixed pts	828 cycles	2 nodes	5.64 avg steps	65 max steps	7.59 avg steps	67 max steps	1,585 final numbers
71	18,474,840	63 fixed pts	686 cycles	2 nodes	5.67 avg steps	69 max steps	7.63 avg steps	71 max steps	1,309 final numbers
72	19,757,815	73 fixed pts	896 cycles	2 nodes	5.76 avg steps	67 max steps	7.72 avg steps	69 max steps	1,719 final numbers
73	21,111,090	66 fixed pts	747 cycles	2 nodes	5.70 avg steps	71 max steps	7.66 avg steps	73 max steps	1,428 final numbers
74	22,537,515	78 fixed pts	969 cycles	2 nodes	5.81 avg steps	69 max steps	7.77 avg steps	71 max steps	1,860 final numbers
75	24,040,016	71 fixed pts	813 cycles	2 nodes	5.65 avg steps	73 max steps	7.62 avg steps	75 max steps	1,555 final numbers
76	25,621,596	81 fixed pts	1,045 cycles	2 nodes	5.88 avg steps	71 max steps	7.84 avg steps	73 max steps	2,009 final numbers
77	27,285,336	73 fixed pts	880 cycles	2 nodes	5.78 avg steps	75 max steps	7.74 avg steps	77 max steps	1,687 final numbers
78	29,034,396	87 fixed pts	1,127 cycles	2 nodes	5.91 avg steps	73 max steps	7.87 avg steps	75 max steps	2,167 final numbers
79	30,872,016	77 fixed pts	952 cycles	2 nodes	5.82 avg steps	77 max steps	7.79 avg steps	79 max steps	1,827 final numbers
80	32,801,517	90 fixed pts	1,211 cycles	2 nodes	5.87 avg steps	75 max steps	7.83 avg steps	77 max steps	2,332 final numbers
81	34,826,302	82 fixed pts	1,029 cycles	2 nodes	5.89 avg steps	79 max steps	7.85 avg steps	81 max steps	1,976 final numbers
82	36,949,857	94 fixed pts	1,299 cycles	2 nodes	5.99 avg steps	77 max steps	7.96 avg steps	79 max steps	2,504 final numbers
83	39,175,752	86 fixed pts	1,109 cycles	2 nodes	5.91 avg steps	81 max steps	7.88 avg steps	83 max steps	2,132 final numbers
84	41,507,642	98 fixed pts	1,392 cycles	2 nodes	6.04 avg steps	79 max steps	8.01 avg steps	81 max steps	2,686 final numbers
85	43,949,268	90 fixed pts	1,193 cycles	2 nodes	5.88 avg steps	83 max steps	7.85 avg steps	85 max steps	2,296 final numbers
86	46,504,458	104 fixed pts	1,490 cycles	2 nodes	6.11 avg steps	81 max steps	8.08 avg steps	83 max steps	2,876 final numbers
87	49,177,128	94 fixed pts	1,281 cycles	2 nodes	6.00 avg steps	85 max steps	7.97 avg steps	87 max steps	2,468 final numbers
88	51,971,283	107 fixed pts	1,591 cycles	2 nodes	6.14 avg steps	83 max steps	8.11 avg steps	85 max steps	3,075 final numbers
89	54,891,018	98 fixed pts	1,373 cycles	2 nodes	6.05 avg steps	87 max steps	8.02 avg steps	89 max steps	2,648 final numbers
90	57,940,519	114 fixed pts	1,699 cycles	2 nodes	6.11 avg steps	85 max steps	8.08 avg steps	87 max steps	3,284 final numbers
91	61,124,064	103 fixed pts	1,470 cycles	2 nodes	6.11 avg steps	89 max steps	8.08 avg steps	91 max steps	2,837 final numbers
92	64,446,024	116 fixed pts	1,808 cycles	2 nodes	6.23 avg steps	87 max steps	8.20 avg steps	89 max steps	3,500 final numbers
93	67,910,864	108 fixed pts	1,572 cycles	2 nodes	6.15 avg steps	91 max steps	8.12 avg steps	93 max steps	3,036 final numbers
94	71,523,144	122 fixed pts	1,924 cycles	2 nodes	6.28 avg steps	89 max steps	8.25 avg steps	91 max steps	3,726 final numbers
95	75,287,520	113 fixed pts	1,678 cycles	2 nodes	6.11 avg steps	93 max steps	8.08 avg steps	95 max steps	3,243 final numbers
96	79,208,745	127 fixed pts	2,045 cycles	2 nodes	6.35 avg steps	91 max steps	8.31 avg steps	93 max steps	3,963 final numbers
97	83,291,670	116 fixed pts	1,787 cycles	2 nodes	6.23 avg steps	95 max steps	8.21 avg steps	97 max steps	3,458 final numbers
98	87,541,245	133 fixed pts	2,171 cycles	2 nodes	6.39 avg steps	93 max steps	8.36 avg steps	95 max steps	4,209 final numbers
99	91,962,520	122 fixed pts	1,903 cycles	2 nodes	6.28 avg steps	97 max steps	8.25 avg steps	99 max steps	3,684 final numbers
100	96,560,646	137 fixed pts	2,301 cycles	2 nodes	6.35 avg steps	95 max steps	8.32 avg steps	97 max steps	4,465 final numbers