Base 15: 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] [Base 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	E

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	15	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	120	0 fixed pts	0 cycles	0 nodes	3.85 avg steps	5 max steps	4.85 avg steps	6 max steps	0 final numbers
3	680	0 fixed pts	1 cycle	2 nodes	3.79 avg steps	8 max steps	5.76 avg steps	10 max steps	2 final numbers
4	3,060	1 fixed pt	7 cycles	4 nodes	2.03 avg steps	4 max steps	5.54 avg steps	8 max steps	21 final numbers
5	11,628	1 fixed pt	1 cycle	1 node	7.20 avg steps	13 max steps	8.20 avg steps	14 max steps	1 final number
6	38,760	0 fixed pts	2 cycles	9 nodes	6.26 avg steps	14 max steps	14.11 avg steps	23 max steps	12 final numbers
7	116,280	0 fixed pts	2 cycles	10 nodes	6.11 avg steps	13 max steps	15.69 avg steps	23 max steps	18 final numbers
8	319,770	1 fixed pt	4 cycles	22 nodes	7.07 avg steps	18 max steps	19.95 avg steps	38 max steps	30 final numbers
9	817,190	1 fixed pt	3 cycles	8 nodes	20.32 avg steps	41 max steps	27.93 avg steps	49 max steps	15 final numbers
10	1,961,256	1 fixed pt	3 cycles	6 nodes	15.69 avg steps	36 max steps	21.68 avg steps	42 max steps	10 final numbers
11	4,457,400	1 fixed pt	4 cycles	11 nodes	12.89 avg steps	37 max steps	18.93 avg steps	41 max steps	25 final numbers
12	9,657,700	0 fixed pts	2 cycles	19 nodes	12.19 avg steps	33 max steps	31.15 avg steps	52 max steps	22 final numbers
13	20,058,300	1 fixed pt	2 cycles	4 nodes	35.10 avg steps	70 max steps	39.10 avg steps	74 max steps	5 final numbers
14	40,116,600	1 fixed pt	4 cycles	7 nodes	19.55 avg steps	61 max steps	25.63 avg steps	67 max steps	17 final numbers
15	77,558,760	3 fixed pts	7 cycles	33 nodes	12.99 avg steps	34 max steps	42.92 avg steps	67 max steps	48 final numbers
16	145,422,675	2 fixed pts	6 cycles	6 nodes	31.03 avg steps	65 max steps	37.01 avg steps	71 max steps	18 final numbers
17	265,182,525	1 fixed pt	5 cycles	11 nodes	18.43 avg steps	44 max steps	24.52 avg steps	49 max steps	26 final numbers
18	471,435,600	2 fixed pts	5 cycles	10 nodes	17.71 avg steps	45 max steps	24.84 avg steps	51 max steps	21 final numbers
19	818,809,200	1 fixed pt	4 cycles	18 nodes	12.49 avg steps	30 max steps	20.84 avg steps	40 max steps	32 final numbers
20	1,391,975,640	2 fixed pts	5 cycles	27 nodes	25.28 avg steps	69 max steps	51.50 avg steps	96 max steps	38 final numbers
21	2,319,959,400	1 fixed pt	3 cycles	11 nodes	14.13 avg steps	39 max steps	22.33 avg steps	47 max steps	20 final numbers
22	3,796,297,200	1 fixed pt	6 cycles	16 nodes	21.65 avg steps	55 max steps	31.46 avg steps	61 max steps	35 final numbers
23	6,107,086,800	5 fixed pts	7 cycles	11 nodes	12.36 avg steps	36 max steps	17.35 avg steps	38 max steps	18 final numbers
24	9,669,554,100	2 fixed pts	9 cycles	16 nodes	29.75 avg steps	84 max steps	33.23 avg steps	87 max steps	46 final numbers