Base 12: 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] [Base 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	B

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	12	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	78	0 fixed pts	1 cycle	6 nodes	1.33 avg steps	2 max steps	6.56 avg steps	8 max steps	6 final numbers
3	364	1 fixed pt	1 cycle	1 node	3.69 avg steps	7 max steps	4.69 avg steps	8 max steps	1 final number
4	1,365	0 fixed pts	2 cycles	6 nodes	3.07 avg steps	7 max steps	8.31 avg steps	13 max steps	9 final numbers
5	4,368	1 fixed pt	2 cycles	2 nodes	6.65 avg steps	12 max steps	7.68 avg steps	13 max steps	3 final numbers
6	12,376	1 fixed pt	2 cycles	10 nodes	7.93 avg steps	19 max steps	17.89 avg steps	29 max steps	11 final numbers
7	31,824	1 fixed pt	2 cycles	9 nodes	10.89 avg steps	24 max steps	19.49 avg steps	33 max steps	10 final numbers
8	75,582	2 fixed pts	3 cycles	24 nodes	8.12 avg steps	24 max steps	30.10 avg steps	48 max steps	26 final numbers
9	167,960	1 fixed pt	4 cycles	13 nodes	6.60 avg steps	18 max steps	18.37 avg steps	31 max steps	24 final numbers
10	352,716	1 fixed pt	4 cycles	5 nodes	12.71 avg steps	36 max steps	17.14 avg steps	40 max steps	13 final numbers
11	705,432	2 fixed pts	4 cycles	21 nodes	8.66 avg steps	25 max steps	23.83 avg steps	46 max steps	29 final numbers
12	1,352,078	2 fixed pts	7 cycles	11 nodes	7.95 avg steps	27 max steps	13.71 avg steps	38 max steps	32 final numbers
13	2,496,144	1 fixed pt	4 cycles	32 nodes	8.15 avg steps	21 max steps	21.23 avg steps	46 max steps	46 final numbers
14	4,457,400	4 fixed pts	12 cycles	5 nodes	7.99 avg steps	34 max steps	12.98 avg steps	39 max steps	44 final numbers
15	7,726,160	2 fixed pts	4 cycles	8 nodes	12.15 avg steps	32 max steps	19.85 avg steps	40 max steps	13 final numbers
16	13,037,895	2 fixed pts	20 cycles	5 nodes	6.89 avg steps	33 max steps	11.89 avg steps	38 max steps	92 final numbers
17	21,474,180	2 fixed pts	4 cycles	8 nodes	14.09 avg steps	38 max steps	22.06 avg steps	46 max steps	18 final numbers
18	34,597,290	5 fixed pts	41 cycles	5 nodes	6.21 avg steps	33 max steps	11.01 avg steps	38 max steps	185 final numbers
19	54,627,300	2 fixed pts	4 cycles	13 nodes	14.16 avg steps	40 max steps	26.84 avg steps	53 max steps	18 final numbers
20	84,672,315	4 fixed pts	71 cycles	5 nodes	6.21 avg steps	33 max steps	11.16 avg steps	38 max steps	339 final numbers
21	129,024,480	6 fixed pts	9 cycles	18 nodes	12.91 avg steps	45 max steps	29.70 avg steps	63 max steps	44 final numbers
22	193,536,720	4 fixed pts	121 cycles	5 nodes	6.06 avg steps	37 max steps	10.97 avg steps	42 max steps	586 final numbers
23	286,097,760	4 fixed pts	6 cycles	23 nodes	13.76 avg steps	50 max steps	36.32 avg steps	73 max steps	50 final numbers
24	417,225,900	5 fixed pts	196 cycles	5 nodes	7.64 avg steps	42 max steps	12.63 avg steps	47 max steps	960 final numbers
25	600,805,296	5 fixed pts	8 cycles	33 nodes	14.26 avg steps	55 max steps	41.44 avg steps	83 max steps	71 final numbers
26	854,992,152	4 fixed pts	307 cycles	5 nodes	7.07 avg steps	47 max steps	11.95 avg steps	52 max steps	1,515 final numbers
27	1,203,322,288	5 fixed pts	11 cycles	43 nodes	14.82 avg steps	60 max steps	44.75 avg steps	93 max steps	101 final numbers
28	1,676,056,044	10 fixed pts	469 cycles	8 nodes	6.57 avg steps	52 max steps	12.19 avg steps	57 max steps	2,311 final numbers
29	2,311,801,440	6 fixed pts	19 cycles	53 nodes	14.99 avg steps	65 max steps	46.33 avg steps	107 max steps	152 final numbers
30	3,159,461,968	6 fixed pts	681 cycles	13 nodes	7.39 avg steps	57 max steps	14.27 avg steps	62 max steps	3,387 final numbers
31	4,280,561,376	5 fixed pts	33 cycles	63 nodes	14.50 avg steps	70 max steps	43.74 avg steps	130 max steps	238 final numbers
32	5,752,004,349	8 fixed pts	975 cycles	18 nodes	7.38 avg steps	62 max steps	16.38 avg steps	67 max steps	4,866 final numbers
33	7,669,339,132	8 fixed pts	62 cycles	73 nodes	13.51 avg steps	75 max steps	39.99 avg steps	147 max steps	383 final numbers