Base 11: Summary: Odd Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets]
[Odd 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]
[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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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