Base 16: 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] [13] [14] [15] [Base 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	D	E	F

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	16	0 fixed pts	0 cycles	0 nodes	0.94 avg steps	1 max steps	1.94 avg steps	2 max steps	0 final numbers
2	136	0 fixed pts	2 cycles	4 nodes	1.38 avg steps	2 max steps	5.02 avg steps	6 max steps	8 final numbers
3	816	1 fixed pt	1 cycle	1 node	4.50 avg steps	9 max steps	5.50 avg steps	10 max steps	1 final number
4	3,876	0 fixed pts	4 cycles	6 nodes	3.26 avg steps	6 max steps	7.87 avg steps	12 max steps	15 final numbers
5	15,504	0 fixed pts	3 cycles	4 nodes	5.08 avg steps	10 max steps	8.37 avg steps	13 max steps	9 final numbers
6	54,264	1 fixed pt	6 cycles	5 nodes	11.92 avg steps	31 max steps	16.83 avg steps	36 max steps	21 final numbers
7	170,544	1 fixed pt	3 cycles	11 nodes	4.86 avg steps	11 max steps	14.48 avg steps	22 max steps	21 final numbers
8	490,314	0 fixed pts	8 cycles	8 nodes	11.81 avg steps	35 max steps	17.42 avg steps	39 max steps	34 final numbers
9	1,307,504	2 fixed pts	5 cycles	8 nodes	7.80 avg steps	19 max steps	14.94 avg steps	26 max steps	23 final numbers
10	3,268,760	1 fixed pt	20 cycles	8 nodes	10.22 avg steps	31 max steps	16.29 avg steps	37 max steps	88 final numbers
11	7,726,160	1 fixed pt	4 cycles	9 nodes	10.53 avg steps	24 max steps	17.32 avg steps	33 max steps	21 final numbers
12	17,383,860	3 fixed pts	39 cycles	8 nodes	9.53 avg steps	27 max steps	15.52 avg steps	35 max steps	167 final numbers
13	37,442,160	1 fixed pt	4 cycles	4 nodes	11.01 avg steps	26 max steps	14.37 avg steps	30 max steps	11 final numbers
14	77,558,760	6 fixed pts	73 cycles	8 nodes	10.12 avg steps	37 max steps	15.92 avg steps	45 max steps	304 final numbers
15	155,117,520	3 fixed pts	6 cycles	15 nodes	14.72 avg steps	40 max steps	28.12 avg steps	55 max steps	22 final numbers
16	300,540,195	7 fixed pts	129 cycles	8 nodes	10.84 avg steps	35 max steps	16.52 avg steps	41 max steps	531 final numbers
17	565,722,720	2 fixed pts	6 cycles	2 nodes	23.63 avg steps	56 max steps	24.73 avg steps	57 max steps	10 final numbers
18	1,037,158,320	12 fixed pts	232 cycles	8 nodes	11.70 avg steps	44 max steps	17.20 avg steps	52 max steps	926 final numbers
19	1,855,967,520	3 fixed pts	10 cycles	6 nodes	24.13 avg steps	56 max steps	26.21 avg steps	58 max steps	21 final numbers
20	3,247,943,160	15 fixed pts	411 cycles	8 nodes	12.61 avg steps	43 max steps	18.04 avg steps	49 max steps	1,615 final numbers
21	5,567,902,560	7 fixed pts	20 cycles	6 nodes	23.95 avg steps	56 max steps	26.43 avg steps	58 max steps	46 final numbers
22	9,364,199,760	21 fixed pts	729 cycles	8 nodes	13.51 avg steps	52 max steps	18.87 avg steps	60 max steps	2,824 final numbers
23	15,471,286,560	5 fixed pts	27 cycles	6 nodes	25.93 avg steps	66 max steps	28.96 avg steps	68 max steps	83 final numbers
24	25,140,840,660	29 fixed pts	1,265 cycles	8 nodes	14.20 avg steps	51 max steps	19.50 avg steps	57 max steps	4,865 final numbers
25	40,225,345,056	6 fixed pts	41 cycles	6 nodes	28.21 avg steps	79 max steps	31.56 avg steps	81 max steps	143 final numbers
26	63,432,274,896	37 fixed pts	2,150 cycles	8 nodes	15.01 avg steps	60 max steps	20.24 avg steps	68 max steps	8,255 final numbers
27	98,672,427,616	9 fixed pts	62 cycles	6 nodes	30.34 avg steps	82 max steps	34.14 avg steps	84 max steps	229 final numbers