Base 13: 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] [11] [12] [Base 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	B	C

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	13	0 fixed pts	0 cycles	0 nodes	0.92 avg steps	1 max steps	1.92 avg steps	2 max steps	0 final numbers
2	91	0 fixed pts	1 cycle	3 nodes	1.99 avg steps	3 max steps	4.57 avg steps	6 max steps	3 final numbers
3	455	0 fixed pts	1 cycle	2 nodes	3.38 avg steps	7 max steps	5.35 avg steps	9 max steps	2 final numbers
4	1,820	0 fixed pts	3 cycles	6 nodes	2.05 avg steps	4 max steps	7.46 avg steps	10 max steps	15 final numbers
5	6,188	0 fixed pts	1 cycle	4 nodes	6.65 avg steps	12 max steps	10.65 avg steps	16 max steps	4 final numbers
6	18,564	1 fixed pt	1 cycle	1 node	11.84 avg steps	20 max steps	12.84 avg steps	21 max steps	1 final number
7	50,388	0 fixed pts	3 cycles	12 nodes	5.99 avg steps	14 max steps	12.22 avg steps	26 max steps	16 final numbers
8	125,970	1 fixed pt	2 cycles	4 nodes	9.44 avg steps	24 max steps	10.96 avg steps	25 max steps	5 final numbers
9	293,930	0 fixed pts	3 cycles	5 nodes	12.98 avg steps	34 max steps	17.98 avg steps	39 max steps	15 final numbers
10	646,646	1 fixed pt	4 cycles	9 nodes	9.81 avg steps	27 max steps	13.24 avg steps	28 max steps	19 final numbers
11	1,352,078	0 fixed pts	1 cycle	14 nodes	14.75 avg steps	43 max steps	28.75 avg steps	57 max steps	14 final numbers
12	2,704,156	1 fixed pt	3 cycles	10 nodes	10.83 avg steps	28 max steps	19.43 avg steps	38 max steps	13 final numbers
13	5,200,300	0 fixed pts	3 cycles	10 nodes	19.65 avg steps	45 max steps	29.56 avg steps	55 max steps	22 final numbers
14	9,657,700	2 fixed pts	3 cycles	15 nodes	9.21 avg steps	31 max steps	22.40 avg steps	46 max steps	17 final numbers
15	17,383,860	0 fixed pts	2 cycles	14 nodes	22.09 avg steps	52 max steps	36.03 avg steps	66 max steps	16 final numbers
16	30,421,755	1 fixed pt	3 cycles	11 nodes	18.83 avg steps	55 max steps	28.62 avg steps	66 max steps	20 final numbers
17	51,895,935	0 fixed pts	4 cycles	23 nodes	14.23 avg steps	47 max steps	36.82 avg steps	70 max steps	44 final numbers
18	86,493,225	1 fixed pt	2 cycles	12 nodes	15.06 avg steps	39 max steps	26.40 avg steps	51 max steps	13 final numbers
19	141,120,525	0 fixed pts	2 cycles	8 nodes	21.67 avg steps	43 max steps	29.67 avg steps	51 max steps	10 final numbers
20	225,792,840	2 fixed pts	5 cycles	12 nodes	12.32 avg steps	29 max steps	21.34 avg steps	41 max steps	24 final numbers
21	354,817,320	0 fixed pts	4 cycles	18 nodes	11.83 avg steps	33 max steps	28.20 avg steps	51 max steps	30 final numbers
22	548,354,040	1 fixed pt	4 cycles	12 nodes	14.83 avg steps	42 max steps	23.65 avg steps	47 max steps	22 final numbers
23	834,451,800	1 fixed pt	4 cycles	15 nodes	15.79 avg steps	34 max steps	17.56 avg steps	35 max steps	24 final numbers
24	1,251,677,700	1 fixed pt	3 cycles	12 nodes	21.79 avg steps	51 max steps	33.25 avg steps	63 max steps	21 final numbers
25	1,852,482,996	2 fixed pts	5 cycles	8 nodes	11.67 avg steps	32 max steps	18.59 avg steps	40 max steps	19 final numbers
26	2,707,475,148	1 fixed pt	3 cycles	12 nodes	18.71 avg steps	53 max steps	26.79 avg steps	65 max steps	15 final numbers
27	3,910,797,436	3 fixed pts	6 cycles	5 nodes	12.27 avg steps	31 max steps	15.44 avg steps	36 max steps	12 final numbers
28	5,586,853,480	2 fixed pts	4 cycles	12 nodes	25.60 avg steps	61 max steps	37.27 avg steps	73 max steps	21 final numbers
29	7,898,654,920	5 fixed pts	9 cycles	5 nodes	11.92 avg steps	35 max steps	15.57 avg steps	40 max steps	17 final numbers