Base 7: 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] [Base 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]
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

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	28	0 fixed pts	0 cycles	0 nodes	2.79 avg steps	4 max steps	3.79 avg steps	5 max steps	0 final numbers
4	210	0 fixed pts	1 cycle	3 nodes	2.36 avg steps	4 max steps	5.29 avg steps	7 max steps	3 final numbers
6	924	0 fixed pts	1 cycle	6 nodes	3.31 avg steps	7 max steps	9.27 avg steps	13 max steps	6 final numbers
8	3,003	0 fixed pts	1 cycle	6 nodes	4.37 avg steps	9 max steps	10.36 avg steps	15 max steps	6 final numbers
10	8,008	0 fixed pts	3 cycles	2 nodes	5.46 avg steps	11 max steps	7.46 avg steps	13 max steps	6 final numbers
12	18,564	0 fixed pts	2 cycles	5 nodes	6.97 avg steps	16 max steps	11.34 avg steps	21 max steps	7 final numbers
14	38,760	0 fixed pts	2 cycles	9 nodes	6.36 avg steps	16 max steps	11.84 avg steps	21 max steps	11 final numbers
16	74,613	0 fixed pts	2 cycles	12 nodes	7.38 avg steps	23 max steps	13.40 avg steps	25 max steps	14 final numbers
18	134,596	0 fixed pts	1 cycle	2 nodes	11.20 avg steps	23 max steps	13.20 avg steps	25 max steps	2 final numbers
20	230,230	1 fixed pt	6 cycles	7 nodes	6.54 avg steps	17 max steps	10.75 avg steps	21 max steps	19 final numbers
22	376,740	2 fixed pts	5 cycles	5 nodes	10.03 avg steps	29 max steps	14.24 avg steps	34 max steps	11 final numbers
24	593,775	3 fixed pts	7 cycles	5 nodes	8.49 avg steps	23 max steps	12.74 avg steps	28 max steps	17 final numbers
26	906,192	4 fixed pts	7 cycles	24 nodes	6.70 avg steps	21 max steps	26.33 avg steps	44 max steps	32 final numbers
28	1,344,904	5 fixed pts	8 cycles	7 nodes	10.92 avg steps	31 max steps	16.61 avg steps	38 max steps	16 final numbers
30	1,947,792	6 fixed pts	12 cycles	25 nodes	7.14 avg steps	25 max steps	26.30 avg steps	50 max steps	42 final numbers
32	2,760,681	7 fixed pts	13 cycles	13 nodes	9.64 avg steps	32 max steps	18.44 avg steps	45 max steps	31 final numbers
34	3,838,380	8 fixed pts	15 cycles	13 nodes	9.70 avg steps	30 max steps	19.35 avg steps	43 max steps	34 final numbers
36	5,245,786	9 fixed pts	16 cycles	3 nodes	17.33 avg steps	51 max steps	18.64 avg steps	52 max steps	24 final numbers
38	7,059,052	11 fixed pts	20 cycles	17 nodes	9.31 avg steps	36 max steps	19.13 avg steps	53 max steps	45 final numbers
40	9,366,819	13 fixed pts	25 cycles	3 nodes	14.24 avg steps	46 max steps	16.50 avg steps	49 max steps	39 final numbers
42	12,271,512	15 fixed pts	29 cycles	11 nodes	13.39 avg steps	53 max steps	19.14 avg steps	64 max steps	54 final numbers
44	15,890,700	17 fixed pts	33 cycles	3 nodes	12.73 avg steps	52 max steps	15.01 avg steps	55 max steps	53 final numbers
46	20,358,520	19 fixed pts	38 cycles	7 nodes	12.00 avg steps	50 max steps	14.60 avg steps	53 max steps	67 final numbers
48	25,827,165	21 fixed pts	42 cycles	3 nodes	11.98 avg steps	57 max steps	14.13 avg steps	60 max steps	70 final numbers
50	32,468,436	23 fixed pts	48 cycles	3 nodes	13.51 avg steps	56 max steps	15.77 avg steps	59 max steps	81 final numbers
52	40,475,358	25 fixed pts	53 cycles	3 nodes	11.44 avg steps	54 max steps	13.67 avg steps	57 max steps	90 final numbers
54	50,063,860	27 fixed pts	57 cycles	3 nodes	13.18 avg steps	61 max steps	15.50 avg steps	64 max steps	97 final numbers
56	61,474,519	30 fixed pts	63 cycles	3 nodes	12.49 avg steps	60 max steps	14.47 avg steps	63 max steps	108 final numbers
58	74,974,368	33 fixed pts	71 cycles	3 nodes	11.31 avg steps	58 max steps	13.57 avg steps	61 max steps	125 final numbers
60	90,858,768	36 fixed pts	79 cycles	3 nodes	11.54 avg steps	65 max steps	13.88 avg steps	68 max steps	140 final numbers
62	109,453,344	39 fixed pts	87 cycles	3 nodes	10.98 avg steps	64 max steps	13.14 avg steps	67 max steps	155 final numbers
64	131,115,985	42 fixed pts	95 cycles	11 nodes	10.35 avg steps	62 max steps	12.97 avg steps	65 max steps	179 final numbers
66	156,238,908	45 fixed pts	101 cycles	3 nodes	10.85 avg steps	69 max steps	13.00 avg steps	72 max steps	181 final numbers
68	185,250,786	48 fixed pts	109 cycles	5 nodes	10.27 avg steps	68 max steps	12.60 avg steps	71 max steps	199 final numbers
70	218,618,940	51 fixed pts	119 cycles	5 nodes	10.29 avg steps	66 max steps	12.60 avg steps	69 max steps	221 final numbers
72	256,851,595	54 fixed pts	132 cycles	5 nodes	9.89 avg steps	73 max steps	12.44 avg steps	76 max steps	252 final numbers
74	300,500,200	58 fixed pts	141 cycles	5 nodes	9.74 avg steps	72 max steps	12.14 avg steps	75 max steps	271 final numbers
76	350,161,812	62 fixed pts	151 cycles	9 nodes	9.29 avg steps	70 max steps	11.80 avg steps	73 max steps	299 final numbers
78	406,481,544	66 fixed pts	161 cycles	5 nodes	9.25 avg steps	77 max steps	11.65 avg steps	80 max steps	317 final numbers
80	470,155,077	70 fixed pts	172 cycles	6 nodes	8.99 avg steps	76 max steps	11.51 avg steps	79 max steps	341 final numbers
82	541,931,236	74 fixed pts	185 cycles	6 nodes	8.91 avg steps	74 max steps	11.38 avg steps	77 max steps	372 final numbers
84	622,614,630	78 fixed pts	195 cycles	6 nodes	8.82 avg steps	81 max steps	11.44 avg steps	84 max steps	397 final numbers
86	713,068,356	82 fixed pts	210 cycles	6 nodes	8.53 avg steps	80 max steps	11.13 avg steps	83 max steps	437 final numbers
88	814,216,767	86 fixed pts	221 cycles	6 nodes	8.41 avg steps	78 max steps	11.11 avg steps	81 max steps	465 final numbers
90	927,048,304	90 fixed pts	234 cycles	6 nodes	8.41 avg steps	85 max steps	11.06 avg steps	88 max steps	497 final numbers
92	1,052,618,392	95 fixed pts	251 cycles	6 nodes	8.16 avg steps	84 max steps	10.88 avg steps	87 max steps	538 final numbers
94	1,192,052,400	100 fixed pts	266 cycles	6 nodes	8.08 avg steps	82 max steps	10.77 avg steps	85 max steps	576 final numbers
96	1,346,548,665	105 fixed pts	280 cycles	6 nodes	8.08 avg steps	89 max steps	10.85 avg steps	92 max steps	611 final numbers
98	1,517,381,580	110 fixed pts	294 cycles	6 nodes	8.24 avg steps	88 max steps	10.95 avg steps	91 max steps	646 final numbers
100	1,705,904,746	115 fixed pts	315 cycles	11 nodes	7.84 avg steps	86 max steps	10.79 avg steps	89 max steps	708 final numbers