Base 6: Summary: Odd Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets]
[Odd 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]
[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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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