Base 11: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [2] [3] [4] [5] [6] [7] [8] [9] [10] [Base 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	8	9	A

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	11	0 fixed pts	0 cycles	0 nodes	0.91 avg steps	1 max steps	1.91 avg steps	2 max steps	0 final numbers
2	66	1 fixed pt	1 cycle	1 node	2.61 avg steps	4 max steps	3.61 avg steps	5 max steps	1 final number
3	286	0 fixed pts	1 cycle	2 nodes	2.97 avg steps	6 max steps	4.93 avg steps	8 max steps	2 final numbers
4	1,001	0 fixed pts	2 cycles	5 nodes	2.14 avg steps	4 max steps	7.10 avg steps	9 max steps	10 final numbers
5	3,003	0 fixed pts	1 cycle	4 nodes	4.17 avg steps	8 max steps	8.16 avg steps	12 max steps	4 final numbers
6	8,008	0 fixed pts	1 cycle	4 nodes	6.53 avg steps	17 max steps	10.53 avg steps	21 max steps	4 final numbers
7	19,448	0 fixed pts	2 cycles	14 nodes	5.95 avg steps	14 max steps	17.18 avg steps	28 max steps	18 final numbers
8	43,758	1 fixed pt	3 cycles	7 nodes	5.27 avg steps	16 max steps	11.23 avg steps	23 max steps	12 final numbers
9	92,378	1 fixed pt	2 cycles	7 nodes	11.92 avg steps	27 max steps	18.71 avg steps	34 max steps	8 final numbers
10	184,756	0 fixed pts	4 cycles	11 nodes	6.15 avg steps	17 max steps	14.77 avg steps	28 max steps	22 final numbers
11	352,716	0 fixed pts	3 cycles	10 nodes	8.35 avg steps	21 max steps	15.35 avg steps	31 max steps	21 final numbers
12	646,646	1 fixed pt	4 cycles	6 nodes	12.53 avg steps	29 max steps	18.31 avg steps	35 max steps	13 final numbers
13	1,144,066	0 fixed pts	2 cycles	5 nodes	10.08 avg steps	24 max steps	15.08 avg steps	29 max steps	10 final numbers
14	1,961,256	0 fixed pts	4 cycles	17 nodes	7.17 avg steps	21 max steps	23.71 avg steps	38 max steps	25 final numbers
15	3,268,760	0 fixed pts	1 cycle	12 nodes	11.08 avg steps	26 max steps	23.08 avg steps	38 max steps	12 final numbers
16	5,311,735	1 fixed pt	5 cycles	19 nodes	9.44 avg steps	24 max steps	28.10 avg steps	43 max steps	28 final numbers
17	8,436,285	1 fixed pt	3 cycles	7 nodes	9.36 avg steps	21 max steps	14.67 avg steps	26 max steps	13 final numbers
18	13,123,110	1 fixed pt	6 cycles	20 nodes	11.28 avg steps	30 max steps	30.95 avg steps	50 max steps	31 final numbers
19	20,030,010	1 fixed pt	3 cycles	5 nodes	9.65 avg steps	30 max steps	13.60 avg steps	35 max steps	8 final numbers
20	30,045,015	1 fixed pt	6 cycles	8 nodes	21.65 avg steps	56 max steps	29.60 avg steps	64 max steps	19 final numbers
21	44,352,165	2 fixed pts	4 cycles	2 nodes	10.47 avg steps	26 max steps	12.25 avg steps	28 max steps	6 final numbers
22	64,512,240	0 fixed pts	7 cycles	24 nodes	14.44 avg steps	41 max steps	34.96 avg steps	61 max steps	48 final numbers
23	92,561,040	2 fixed pts	6 cycles	2 nodes	9.21 avg steps	27 max steps	11.20 avg steps	29 max steps	10 final numbers
24	131,128,140	1 fixed pt	7 cycles	12 nodes	16.86 avg steps	52 max steps	28.82 avg steps	64 max steps	25 final numbers
25	183,579,396	3 fixed pts	9 cycles	2 nodes	8.51 avg steps	22 max steps	10.11 avg steps	23 max steps	15 final numbers
26	254,186,856	1 fixed pt	10 cycles	22 nodes	12.40 avg steps	36 max steps	31.51 avg steps	57 max steps	56 final numbers
27	348,330,136	4 fixed pts	14 cycles	2 nodes	7.97 avg steps	24 max steps	9.96 avg steps	26 max steps	24 final numbers
28	472,733,756	2 fixed pts	10 cycles	45 nodes	10.93 avg steps	52 max steps	54.30 avg steps	97 max steps	68 final numbers
29	635,745,396	4 fixed pts	20 cycles	16 nodes	7.27 avg steps	27 max steps	10.44 avg steps	39 max steps	50 final numbers
30	847,660,528	1 fixed pt	11 cycles	17 nodes	15.93 avg steps	52 max steps	31.40 avg steps	68 max steps	58 final numbers
31	1,121,099,408	4 fixed pts	27 cycles	6 nodes	7.28 avg steps	27 max steps	9.50 avg steps	29 max steps	54 final numbers
32	1,471,442,973	3 fixed pts	12 cycles	15 nodes	22.15 avg steps	65 max steps	30.10 avg steps	66 max steps	48 final numbers
33	1,917,334,783	5 fixed pts	35 cycles	2 nodes	7.51 avg steps	27 max steps	9.39 avg steps	29 max steps	65 final numbers
34	2,481,256,778	2 fixed pts	12 cycles	12 nodes	22.75 avg steps	62 max steps	29.21 avg steps	64 max steps	34 final numbers
35	3,190,187,286	6 fixed pts	46 cycles	2 nodes	7.92 avg steps	31 max steps	9.90 avg steps	33 max steps	86 final numbers
36	4,076,350,421	5 fixed pts	15 cycles	4 nodes	41.38 avg steps	109 max steps	42.58 avg steps	110 max steps	27 final numbers
37	5,178,066,751	7 fixed pts	60 cycles	3 nodes	7.21 avg steps	32 max steps	9.26 avg steps	34 max steps	115 final numbers
38	6,540,715,896	3 fixed pts	18 cycles	6 nodes	23.29 avg steps	65 max steps	25.43 avg steps	67 max steps	43 final numbers
39	8,217,822,536	7 fixed pts	74 cycles	6 nodes	6.98 avg steps	33 max steps	9.82 avg steps	39 max steps	147 final numbers