Base 5: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Summary
[All Digit Sets] — [2] [3] [4] [Base 5] [6] [7] [8] [9] [10] [11] [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

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	5	0 fixed pts	0 cycles	0 nodes	0.80 avg steps	1 max steps	1.80 avg steps	2 max steps	0 final numbers
2	15	1 fixed pt	1 cycle	1 node	1.60 avg steps	3 max steps	2.60 avg steps	4 max steps	1 final number
3	35	0 fixed pts	1 cycle	2 nodes	1.57 avg steps	3 max steps	3.43 avg steps	5 max steps	2 final numbers
4	70	1 fixed pt	1 cycle	1 node	2.43 avg steps	4 max steps	3.43 avg steps	5 max steps	1 final number
5	126	0 fixed pts	1 cycle	4 nodes	1.79 avg steps	3 max steps	5.67 avg steps	7 max steps	4 final numbers
6	210	0 fixed pts	1 cycle	5 nodes	2.23 avg steps	5 max steps	7.13 avg steps	10 max steps	5 final numbers
7	330	0 fixed pts	1 cycle	4 nodes	3.45 avg steps	7 max steps	7.41 avg steps	11 max steps	4 final numbers
8	495	0 fixed pts	1 cycle	6 nodes	3.04 avg steps	8 max steps	8.99 avg steps	14 max steps	6 final numbers
9	715	1 fixed pt	1 cycle	1 node	8.01 avg steps	14 max steps	9.01 avg steps	15 max steps	1 final number
10	1,001	0 fixed pts	1 cycle	4 nodes	4.21 avg steps	9 max steps	8.20 avg steps	13 max steps	4 final numbers
11	1,365	1 fixed pt	2 cycles	3 nodes	6.47 avg steps	14 max steps	9.42 avg steps	17 max steps	4 final numbers
12	1,820	0 fixed pts	1 cycle	8 nodes	6.41 avg steps	16 max steps	14.39 avg steps	24 max steps	8 final numbers
13	2,380	1 fixed pt	3 cycles	5 nodes	5.95 avg steps	14 max steps	10.79 avg steps	19 max steps	9 final numbers
14	3,060	0 fixed pts	2 cycles	5 nodes	4.48 avg steps	13 max steps	9.27 avg steps	18 max steps	9 final numbers
15	3,876	1 fixed pt	6 cycles	6 nodes	4.27 avg steps	11 max steps	9.30 avg steps	17 max steps	21 final numbers
16	4,845	1 fixed pt	3 cycles	5 nodes	8.11 avg steps	21 max steps	11.64 avg steps	25 max steps	10 final numbers
17	5,985	1 fixed pt	9 cycles	6 nodes	4.54 avg steps	12 max steps	8.47 avg steps	16 max steps	29 final numbers
18	7,315	1 fixed pt	2 cycles	5 nodes	8.06 avg steps	24 max steps	12.94 avg steps	29 max steps	6 final numbers
19	8,855	1 fixed pt	14 cycles	6 nodes	4.01 avg steps	16 max steps	7.97 avg steps	20 max steps	48 final numbers
20	10,626	1 fixed pt	2 cycles	3 nodes	8.51 avg steps	22 max steps	11.47 avg steps	25 max steps	4 final numbers
21	12,650	1 fixed pt	16 cycles	9 nodes	4.77 avg steps	20 max steps	11.81 avg steps	29 max steps	66 final numbers
22	14,950	1 fixed pt	4 cycles	5 nodes	6.49 avg steps	21 max steps	11.21 avg steps	26 max steps	14 final numbers
23	17,550	2 fixed pts	23 cycles	9 nodes	4.00 avg steps	15 max steps	9.45 avg steps	21 max steps	93 final numbers
24	20,475	1 fixed pt	4 cycles	11 nodes	6.09 avg steps	25 max steps	12.32 avg steps	30 max steps	20 final numbers
25	23,751	2 fixed pts	26 cycles	11 nodes	3.54 avg steps	11 max steps	12.12 avg steps	22 max steps	126 final numbers
26	27,405	1 fixed pt	4 cycles	10 nodes	6.44 avg steps	25 max steps	14.87 avg steps	30 max steps	19 final numbers
27	31,465	2 fixed pts	30 cycles	11 nodes	3.40 avg steps	12 max steps	12.05 avg steps	22 max steps	166 final numbers
28	35,960	1 fixed pt	5 cycles	6 nodes	7.80 avg steps	25 max steps	12.29 avg steps	30 max steps	17 final numbers
29	40,920	2 fixed pts	36 cycles	11 nodes	3.31 avg steps	12 max steps	11.57 avg steps	21 max steps	214 final numbers
30	46,376	2 fixed pts	7 cycles	9 nodes	7.07 avg steps	25 max steps	13.82 avg steps	31 max steps	27 final numbers
31	52,360	2 fixed pts	40 cycles	14 nodes	3.23 avg steps	13 max steps	14.06 avg steps	27 max steps	270 final numbers
32	58,905	2 fixed pts	11 cycles	6 nodes	6.86 avg steps	25 max steps	10.55 avg steps	30 max steps	34 final numbers
33	66,045	2 fixed pts	54 cycles	14 nodes	3.05 avg steps	12 max steps	10.55 avg steps	22 max steps	339 final numbers
34	73,815	2 fixed pts	11 cycles	6 nodes	8.87 avg steps	25 max steps	13.90 avg steps	30 max steps	36 final numbers
35	82,251	2 fixed pts	68 cycles	14 nodes	3.07 avg steps	13 max steps	10.10 avg steps	22 max steps	410 final numbers
36	91,390	2 fixed pts	14 cycles	6 nodes	6.98 avg steps	25 max steps	10.94 avg steps	30 max steps	46 final numbers
37	101,270	3 fixed pts	77 cycles	14 nodes	2.98 avg steps	11 max steps	11.94 avg steps	23 max steps	495 final numbers
38	111,930	2 fixed pts	16 cycles	6 nodes	6.83 avg steps	25 max steps	10.60 avg steps	30 max steps	55 final numbers
39	123,410	3 fixed pts	83 cycles	18 nodes	2.92 avg steps	11 max steps	14.53 avg steps	29 max steps	591 final numbers
40	135,751	2 fixed pts	18 cycles	9 nodes	6.39 avg steps	25 max steps	12.29 avg steps	30 max steps	70 final numbers
41	148,995	3 fixed pts	95 cycles	18 nodes	2.87 avg steps	12 max steps	13.03 avg steps	25 max steps	699 final numbers
42	163,185	2 fixed pts	19 cycles	12 nodes	6.29 avg steps	25 max steps	14.11 avg steps	30 max steps	82 final numbers
43	178,365	3 fixed pts	107 cycles	18 nodes	2.84 avg steps	14 max steps	12.94 avg steps	25 max steps	819 final numbers
44	194,580	3 fixed pts	25 cycles	9 nodes	6.22 avg steps	25 max steps	11.20 avg steps	30 max steps	97 final numbers
45	211,876	3 fixed pts	126 cycles	18 nodes	2.81 avg steps	12 max steps	11.90 avg steps	25 max steps	952 final numbers
46	230,300	3 fixed pts	27 cycles	9 nodes	6.51 avg steps	25 max steps	11.51 avg steps	30 max steps	107 final numbers
47	249,900	3 fixed pts	144 cycles	18 nodes	2.71 avg steps	11 max steps	12.56 avg steps	25 max steps	1,103 final numbers
48	270,725	3 fixed pts	29 cycles	11 nodes	5.72 avg steps	25 max steps	13.32 avg steps	30 max steps	135 final numbers
49	292,825	3 fixed pts	150 cycles	23 nodes	2.71 avg steps	12 max steps	16.52 avg steps	35 max steps	1,260 final numbers
50	316,251	3 fixed pts	30 cycles	11 nodes	6.57 avg steps	25 max steps	13.20 avg steps	30 max steps	142 final numbers
51	341,055	4 fixed pts	160 cycles	23 nodes	2.68 avg steps	13 max steps	17.03 avg steps	34 max steps	1,436 final numbers
52	367,290	3 fixed pts	33 cycles	11 nodes	6.07 avg steps	25 max steps	14.11 avg steps	32 max steps	175 final numbers
53	395,010	4 fixed pts	188 cycles	23 nodes	2.66 avg steps	12 max steps	14.10 avg steps	31 max steps	1,628 final numbers
54	424,270	3 fixed pts	35 cycles	11 nodes	6.90 avg steps	27 max steps	13.08 avg steps	33 max steps	183 final numbers
55	455,126	4 fixed pts	196 cycles	26 nodes	2.64 avg steps	12 max steps	18.66 avg steps	38 max steps	1,836 final numbers
56	487,635	3 fixed pts	41 cycles	11 nodes	5.87 avg steps	25 max steps	13.41 avg steps	34 max steps	231 final numbers
57	521,855	4 fixed pts	209 cycles	26 nodes	2.62 avg steps	16 max steps	17.99 avg steps	36 max steps	2,061 final numbers
58	557,845	4 fixed pts	42 cycles	11 nodes	7.46 avg steps	25 max steps	12.87 avg steps	34 max steps	232 final numbers
59	595,665	4 fixed pts	238 cycles	26 nodes	2.59 avg steps	15 max steps	15.82 avg steps	35 max steps	2,304 final numbers
60	635,376	4 fixed pts	46 cycles	14 nodes	5.70 avg steps	25 max steps	15.14 avg steps	34 max steps	288 final numbers
61	677,040	4 fixed pts	247 cycles	29 nodes	2.56 avg steps	13 max steps	20.28 avg steps	42 max steps	2,565 final numbers
62	720,720	4 fixed pts	50 cycles	14 nodes	5.97 avg steps	25 max steps	12.73 avg steps	34 max steps	300 final numbers
63	766,480	4 fixed pts	257 cycles	30 nodes	2.54 avg steps	12 max steps	21.68 avg steps	42 max steps	2,845 final numbers
64	814,385	4 fixed pts	63 cycles	14 nodes	5.36 avg steps	25 max steps	12.21 avg steps	34 max steps	365 final numbers
65	864,501	5 fixed pts	313 cycles	30 nodes	2.53 avg steps	13 max steps	17.25 avg steps	39 max steps	3,145 final numbers
66	916,895	4 fixed pts	64 cycles	14 nodes	6.84 avg steps	26 max steps	14.00 avg steps	34 max steps	372 final numbers
67	971,635	5 fixed pts	367 cycles	30 nodes	2.51 avg steps	14 max steps	16.32 avg steps	39 max steps	3,465 final numbers
68	1,028,790	4 fixed pts	78 cycles	14 nodes	5.75 avg steps	25 max steps	12.22 avg steps	34 max steps	440 final numbers
69	1,088,430	5 fixed pts	378 cycles	33 nodes	2.50 avg steps	14 max steps	21.28 avg steps	47 max steps	3,806 final numbers
70	1,150,626	4 fixed pts	82 cycles	14 nodes	6.04 avg steps	25 max steps	12.02 avg steps	34 max steps	456 final numbers
71	1,215,450	5 fixed pts	397 cycles	33 nodes	2.48 avg steps	15 max steps	20.13 avg steps	43 max steps	4,169 final numbers
72	1,282,975	5 fixed pts	91 cycles	14 nodes	5.37 avg steps	25 max steps	13.10 avg steps	34 max steps	541 final numbers
73	1,353,275	5 fixed pts	408 cycles	35 nodes	2.46 avg steps	12 max steps	23.46 avg steps	47 max steps	4,554 final numbers
74	1,426,425	5 fixed pts	92 cycles	14 nodes	6.37 avg steps	25 max steps	12.57 avg steps	34 max steps	544 final numbers
75	1,502,501	5 fixed pts	456 cycles	35 nodes	2.45 avg steps	12 max steps	19.47 avg steps	44 max steps	4,962 final numbers
76	1,581,580	5 fixed pts	98 cycles	18 nodes	5.28 avg steps	25 max steps	14.63 avg steps	34 max steps	640 final numbers
77	1,663,740	5 fixed pts	484 cycles	35 nodes	2.44 avg steps	13 max steps	20.51 avg steps	44 max steps	5,394 final numbers
78	1,749,060	5 fixed pts	101 cycles	18 nodes	5.48 avg steps	25 max steps	13.66 avg steps	34 max steps	661 final numbers
79	1,837,620	6 fixed pts	502 cycles	35 nodes	2.43 avg steps	15 max steps	22.58 avg steps	45 max steps	5,850 final numbers
80	1,929,501	5 fixed pts	113 cycles	18 nodes	5.02 avg steps	25 max steps	13.74 avg steps	34 max steps	769 final numbers
81	2,024,785	6 fixed pts	515 cycles	39 nodes	2.42 avg steps	12 max steps	25.13 avg steps	51 max steps	6,331 final numbers
82	2,123,555	5 fixed pts	114 cycles	18 nodes	6.30 avg steps	28 max steps	14.44 avg steps	35 max steps	776 final numbers
83	2,225,895	6 fixed pts	538 cycles	39 nodes	2.41 avg steps	13 max steps	24.13 avg steps	48 max steps	6,838 final numbers
84	2,331,890	5 fixed pts	125 cycles	18 nodes	5.18 avg steps	25 max steps	14.06 avg steps	34 max steps	889 final numbers
85	2,441,626	6 fixed pts	551 cycles	41 nodes	2.40 avg steps	12 max steps	27.31 avg steps	53 max steps	7,371 final numbers
86	2,555,190	6 fixed pts	132 cycles	18 nodes	5.29 avg steps	25 max steps	13.08 avg steps	34 max steps	916 final numbers
87	2,672,670	6 fixed pts	627 cycles	41 nodes	2.39 avg steps	12 max steps	22.77 avg steps	50 max steps	7,931 final numbers
88	2,794,155	6 fixed pts	151 cycles	18 nodes	4.95 avg steps	25 max steps	12.91 avg steps	34 max steps	1,049 final numbers
89	2,919,735	6 fixed pts	651 cycles	41 nodes	2.38 avg steps	12 max steps	24.85 avg steps	50 max steps	8,519 final numbers
90	3,049,501	6 fixed pts	152 cycles	18 nodes	6.23 avg steps	30 max steps	13.74 avg steps	35 max steps	1,054 final numbers
91	3,183,545	6 fixed pts	707 cycles	41 nodes	2.37 avg steps	12 max steps	22.61 avg steps	50 max steps	9,135 final numbers
92	3,321,960	6 fixed pts	169 cycles	18 nodes	4.87 avg steps	25 max steps	13.34 avg steps	34 max steps	1,201 final numbers
93	3,464,840	7 fixed pts	768 cycles	41 nodes	2.36 avg steps	13 max steps	21.91 avg steps	50 max steps	9,780 final numbers
94	3,612,280	6 fixed pts	172 cycles	18 nodes	5.03 avg steps	25 max steps	13.75 avg steps	34 max steps	1,234 final numbers
95	3,764,376	7 fixed pts	845 cycles	41 nodes	2.35 avg steps	13 max steps	20.91 avg steps	50 max steps	10,455 final numbers
96	3,921,225	6 fixed pts	180 cycles	23 nodes	4.68 avg steps	25 max steps	15.76 avg steps	37 max steps	1,399 final numbers
97	4,082,925	7 fixed pts	868 cycles	41 nodes	2.34 avg steps	13 max steps	24.16 avg steps	50 max steps	11,160 final numbers
98	4,249,575	6 fixed pts	180 cycles	23 nodes	5.30 avg steps	25 max steps	15.76 avg steps	37 max steps	1,409 final numbers
99	4,421,275	7 fixed pts	900 cycles	41 nodes	2.34 avg steps	14 max steps	23.45 avg steps	50 max steps	11,896 final numbers
100	4,598,126	7 fixed pts	189 cycles	23 nodes	4.99 avg steps	25 max steps	17.27 avg steps	40 max steps	1,571 final numbers