Base 14: 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] [Base 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	D

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	14	0 fixed pts	0 cycles	0 nodes	0.93 avg steps	1 max steps	1.93 avg steps	2 max steps	0 final numbers
2	105	1 fixed pt	3 cycles	4 nodes	1.35 avg steps	2 max steps	4.09 avg steps	6 max steps	7 final numbers
3	560	1 fixed pt	1 cycle	1 node	4.10 avg steps	8 max steps	5.10 avg steps	9 max steps	1 final number
4	2,380	0 fixed pts	1 cycle	3 nodes	4.18 avg steps	9 max steps	7.17 avg steps	12 max steps	3 final numbers
5	8,568	0 fixed pts	2 cycles	4 nodes	4.76 avg steps	11 max steps	8.71 avg steps	15 max steps	6 final numbers
6	27,132	1 fixed pt	4 cycles	12 nodes	12.09 avg steps	29 max steps	22.65 avg steps	41 max steps	17 final numbers
7	77,520	0 fixed pts	1 cycle	8 nodes	7.13 avg steps	16 max steps	15.13 avg steps	24 max steps	8 final numbers
8	203,490	1 fixed pt	4 cycles	8 nodes	15.84 avg steps	37 max steps	18.52 avg steps	38 max steps	21 final numbers
9	497,420	2 fixed pts	3 cycles	8 nodes	12.61 avg steps	26 max steps	20.53 avg steps	34 max steps	10 final numbers
10	1,144,066	0 fixed pts	6 cycles	6 nodes	11.36 avg steps	44 max steps	17.24 avg steps	50 max steps	34 final numbers
11	2,496,144	0 fixed pts	3 cycles	10 nodes	9.12 avg steps	23 max steps	15.12 avg steps	28 max steps	17 final numbers
12	5,200,300	1 fixed pt	14 cycles	12 nodes	8.47 avg steps	40 max steps	14.47 avg steps	46 max steps	74 final numbers
13	10,400,600	1 fixed pt	3 cycles	17 nodes	13.24 avg steps	32 max steps	29.30 avg steps	49 max steps	21 final numbers
14	20,058,300	2 fixed pts	24 cycles	12 nodes	7.26 avg steps	47 max steps	13.26 avg steps	53 max steps	142 final numbers
15	37,442,160	2 fixed pts	3 cycles	13 nodes	23.34 avg steps	67 max steps	36.29 avg steps	80 max steps	15 final numbers
16	67,863,915	1 fixed pt	42 cycles	12 nodes	6.68 avg steps	52 max steps	12.72 avg steps	58 max steps	257 final numbers
17	119,759,850	0 fixed pts	1 cycle	32 nodes	12.45 avg steps	32 max steps	44.45 avg steps	64 max steps	32 final numbers
18	206,253,075	3 fixed pts	75 cycles	12 nodes	6.31 avg steps	59 max steps	12.36 avg steps	65 max steps	454 final numbers
19	347,373,600	1 fixed pt	4 cycles	25 nodes	10.97 avg steps	34 max steps	29.65 avg steps	59 max steps	48 final numbers
20	573,166,440	2 fixed pts	127 cycles	12 nodes	6.15 avg steps	64 max steps	12.11 avg steps	70 max steps	774 final numbers
21	927,983,760	1 fixed pt	3 cycles	24 nodes	14.04 avg steps	34 max steps	36.65 avg steps	58 max steps	33 final numbers
22	1,476,337,800	2 fixed pts	211 cycles	12 nodes	6.12 avg steps	71 max steps	12.11 avg steps	77 max steps	1,295 final numbers
23	2,310,789,600	1 fixed pt	4 cycles	14 nodes	17.11 avg steps	52 max steps	26.35 avg steps	60 max steps	31 final numbers
24	3,562,467,300	3 fixed pts	353 cycles	12 nodes	6.02 avg steps	76 max steps	11.91 avg steps	82 max steps	2,127 final numbers
25	5,414,950,296	0 fixed pts	3 cycles	11 nodes	18.53 avg steps	50 max steps	28.32 avg steps	61 max steps	27 final numbers
26	8,122,425,444	4 fixed pts	557 cycles	12 nodes	6.12 avg steps	83 max steps	11.98 avg steps	89 max steps	3,378 final numbers