Base 10: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

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

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	10	0 fixed pts	0 cycles	0 nodes	0.90 avg steps	1 max steps	1.90 avg steps	2 max steps	0 final numbers
2	55	0 fixed pts	1 cycle	5 nodes	1.29 avg steps	2 max steps	5.56 avg steps	7 max steps	5 final numbers
3	220	1 fixed pt	1 cycle	1 node	3.27 avg steps	6 max steps	4.27 avg steps	7 max steps	1 final number
4	715	1 fixed pt	1 cycle	1 node	4.65 avg steps	7 max steps	5.65 avg steps	8 max steps	1 final number
5	2,002	0 fixed pts	3 cycles	4 nodes	2.78 avg steps	6 max steps	6.65 avg steps	10 max steps	10 final numbers
6	5,005	2 fixed pts	3 cycles	7 nodes	5.57 avg steps	13 max steps	12.10 avg steps	20 max steps	9 final numbers
7	11,440	0 fixed pts	1 cycle	8 nodes	5.80 avg steps	13 max steps	13.80 avg steps	21 max steps	8 final numbers
8	24,310	2 fixed pts	4 cycles	7 nodes	7.64 avg steps	19 max steps	12.50 avg steps	22 max steps	12 final numbers
9	48,620	2 fixed pts	3 cycles	14 nodes	5.76 avg steps	13 max steps	19.11 avg steps	27 max steps	16 final numbers
10	92,378	3 fixed pts	8 cycles	7 nodes	6.88 avg steps	17 max steps	10.68 avg steps	20 max steps	22 final numbers
11	167,960	1 fixed pt	3 cycles	8 nodes	6.25 avg steps	16 max steps	11.97 avg steps	21 max steps	14 final numbers
12	293,930	5 fixed pts	16 cycles	7 nodes	6.67 avg steps	18 max steps	10.34 avg steps	21 max steps	42 final numbers
13	497,420	1 fixed pt	5 cycles	5 nodes	5.77 avg steps	17 max steps	10.42 avg steps	22 max steps	18 final numbers
14	817,190	6 fixed pts	27 cycles	7 nodes	7.07 avg steps	25 max steps	10.55 avg steps	28 max steps	73 final numbers
15	1,307,504	2 fixed pts	8 cycles	5 nodes	5.34 avg steps	14 max steps	10.24 avg steps	19 max steps	29 final numbers
16	2,042,975	8 fixed pts	46 cycles	7 nodes	6.73 avg steps	26 max steps	10.28 avg steps	29 max steps	125 final numbers
17	3,124,550	2 fixed pts	9 cycles	5 nodes	6.09 avg steps	18 max steps	10.98 avg steps	23 max steps	34 final numbers
18	4,686,825	12 fixed pts	73 cycles	7 nodes	6.59 avg steps	23 max steps	9.93 avg steps	30 max steps	199 final numbers
19	6,906,900	3 fixed pts	11 cycles	5 nodes	8.18 avg steps	21 max steps	11.69 avg steps	23 max steps	38 final numbers
20	10,015,005	14 fixed pts	110 cycles	7 nodes	6.29 avg steps	28 max steps	9.56 avg steps	31 max steps	308 final numbers
21	14,307,150	5 fixed pts	16 cycles	5 nodes	8.81 avg steps	22 max steps	11.65 avg steps	23 max steps	49 final numbers
22	20,160,075	17 fixed pts	162 cycles	7 nodes	5.89 avg steps	32 max steps	9.41 avg steps	35 max steps	462 final numbers
23	28,048,800	7 fixed pts	25 cycles	5 nodes	8.30 avg steps	22 max steps	11.21 avg steps	25 max steps	71 final numbers
24	38,567,100	21 fixed pts	231 cycles	7 nodes	5.73 avg steps	35 max steps	9.33 avg steps	38 max steps	665 final numbers
25	52,451,256	8 fixed pts	37 cycles	5 nodes	7.55 avg steps	22 max steps	10.43 avg steps	25 max steps	105 final numbers
26	70,607,460	25 fixed pts	318 cycles	7 nodes	5.83 avg steps	35 max steps	9.50 avg steps	38 max steps	920 final numbers
27	94,143,280	12 fixed pts	58 cycles	5 nodes	6.78 avg steps	22 max steps	9.67 avg steps	25 max steps	161 final numbers
28	124,403,620	30 fixed pts	429 cycles	7 nodes	6.69 avg steps	35 max steps	9.83 avg steps	38 max steps	1,243 final numbers
29	163,011,640	14 fixed pts	88 cycles	5 nodes	6.19 avg steps	22 max steps	9.13 avg steps	25 max steps	249 final numbers
30	211,915,132	36 fixed pts	572 cycles	7 nodes	6.99 avg steps	35 max steps	9.87 avg steps	38 max steps	1,658 final numbers
31	273,438,880	17 fixed pts	132 cycles	5 nodes	5.76 avg steps	22 max steps	8.90 avg steps	25 max steps	379 final numbers
32	350,343,565	43 fixed pts	747 cycles	7 nodes	6.77 avg steps	35 max steps	9.73 avg steps	38 max steps	2,170 final numbers
33	445,891,810	21 fixed pts	192 cycles	5 nodes	5.48 avg steps	22 max steps	8.70 avg steps	25 max steps	555 final numbers
34	563,921,995	49 fixed pts	963 cycles	7 nodes	6.51 avg steps	35 max steps	9.46 avg steps	38 max steps	2,806 final numbers
35	708,930,508	25 fixed pts	269 cycles	5 nodes	5.41 avg steps	22 max steps	8.70 avg steps	25 max steps	780 final numbers
36	886,163,135	58 fixed pts	1,229 cycles	7 nodes	6.23 avg steps	35 max steps	9.17 avg steps	38 max steps	3,587 final numbers
37	1,101,716,330	31 fixed pts	372 cycles	5 nodes	5.71 avg steps	22 max steps	8.71 avg steps	25 max steps	1,075 final numbers
38	1,362,649,145	66 fixed pts	1,551 cycles	7 nodes	5.91 avg steps	35 max steps	8.88 avg steps	38 max steps	4,539 final numbers
39	1,677,106,640	36 fixed pts	500 cycles	5 nodes	5.78 avg steps	23 max steps	8.67 avg steps	25 max steps	1,449 final numbers
40	2,054,455,634	75 fixed pts	1,939 cycles	7 nodes	5.65 avg steps	36 max steps	8.74 avg steps	39 max steps	5,689 final numbers
41	2,505,433,700	43 fixed pts	662 cycles	5 nodes	5.60 avg steps	23 max steps	8.55 avg steps	26 max steps	1,922 final numbers
42	3,042,312,350	85 fixed pts	2,401 cycles	7 nodes	5.49 avg steps	37 max steps	8.62 avg steps	40 max steps	7,059 final numbers
43	3,679,075,400	49 fixed pts	864 cycles	5 nodes	5.39 avg steps	23 max steps	8.35 avg steps	26 max steps	2,516 final numbers
44	4,431,613,550	96 fixed pts	2,948 cycles	7 nodes	5.44 avg steps	39 max steps	8.62 avg steps	42 max steps	8,677 final numbers
45	5,317,936,260	58 fixed pts	1,115 cycles	5 nodes	5.20 avg steps	22 max steps	8.15 avg steps	25 max steps	3,252 final numbers
46	6,358,402,050	109 fixed pts	3,586 cycles	7 nodes	5.63 avg steps	40 max steps	8.63 avg steps	43 max steps	10,566 final numbers
47	7,575,968,400	66 fixed pts	1,421 cycles	5 nodes	5.02 avg steps	22 max steps	7.98 avg steps	25 max steps	4,156 final numbers
48	8,996,462,475	121 fixed pts	4,330 cycles	7 nodes	5.69 avg steps	42 max steps	8.61 avg steps	45 max steps	12,774 final numbers
49	10,648,873,950	75 fixed pts	1,792 cycles	5 nodes	4.87 avg steps	22 max steps	7.91 avg steps	25 max steps	5,255 final numbers
50	12,565,671,261	136 fixed pts	5,194 cycles	7 nodes	5.56 avg steps	43 max steps	8.53 avg steps	46 max steps	15,337 final numbers
51	14,783,142,660	86 fixed pts	2,240 cycles	5 nodes	4.75 avg steps	22 max steps	7.82 avg steps	25 max steps	6,578 final numbers
52	17,341,763,505	150 fixed pts	6,191 cycles	7 nodes	5.42 avg steps	45 max steps	8.39 avg steps	48 max steps	18,300 final numbers
53	20,286,591,270	96 fixed pts	2,764 cycles	5 nodes	4.73 avg steps	22 max steps	7.84 avg steps	25 max steps	8,132 final numbers
54	23,667,689,815	167 fixed pts	7,338 cycles	7 nodes	5.29 avg steps	46 max steps	8.25 avg steps	49 max steps	21,708 final numbers
55	27,540,584,512	109 fixed pts	3,382 cycles	5 nodes	4.85 avg steps	22 max steps	7.84 avg steps	27 max steps	9,961 final numbers
56	31,966,749,880	184 fixed pts	8,650 cycles	7 nodes	5.16 avg steps	48 max steps	8.13 avg steps	51 max steps	25,612 final numbers
57	37,014,131,440	121 fixed pts	4,105 cycles	5 nodes	4.89 avg steps	24 max steps	7.83 avg steps	25 max steps	12,106 final numbers
58	42,757,703,560	202 fixed pts	10,149 cycles	7 nodes	5.04 avg steps	49 max steps	8.07 avg steps	52 max steps	30,073 final numbers
59	49,280,065,120	136 fixed pts	4,947 cycles	5 nodes	4.80 avg steps	23 max steps	7.77 avg steps	26 max steps	14,603 final numbers
60	56,672,074,888	222 fixed pts	11,844 cycles	7 nodes	4.95 avg steps	51 max steps	8.01 avg steps	54 max steps	35,123 final numbers
61	65,033,528,560	150 fixed pts	5,921 cycles	5 nodes	4.70 avg steps	25 max steps	7.68 avg steps	28 max steps	17,497 final numbers
62	74,473,879,480	242 fixed pts	13,756 cycles	7 nodes	4.93 avg steps	52 max steps	8.01 avg steps	55 max steps	40,821 final numbers
63	85,113,005,120	167 fixed pts	7,044 cycles	5 nodes	4.62 avg steps	25 max steps	7.59 avg steps	28 max steps	20,833 final numbers
64	97,082,021,465	265 fixed pts	15,908 cycles	7 nodes	5.02 avg steps	54 max steps	8.01 avg steps	57 max steps	47,232 final numbers
65	110,524,147,514	185 fixed pts	8,336 cycles	5 nodes	4.53 avg steps	24 max steps	7.50 avg steps	27 max steps	24,671 final numbers
66	125,595,622,175	287 fixed pts	18,321 cycles	7 nodes	5.03 avg steps	55 max steps	7.99 avg steps	58 max steps	54,427 final numbers
67	142,466,675,900	202 fixed pts	9,804 cycles	5 nodes	4.45 avg steps	22 max steps	7.47 avg steps	25 max steps	29,045 final numbers
68	161,322,559,475	313 fixed pts	21,020 cycles	7 nodes	4.96 avg steps	57 max steps	7.94 avg steps	60 max steps	62,473 final numbers
69	182,364,632,450	222 fixed pts	11,472 cycles	5 nodes	4.39 avg steps	22 max steps	7.43 avg steps	25 max steps	34,014 final numbers
70	205,811,513,765	338 fixed pts	24,028 cycles	7 nodes	4.88 avg steps	58 max steps	7.86 avg steps	61 max steps	71,447 final numbers
71	231,900,297,200	242 fixed pts	13,356 cycles	5 nodes	4.38 avg steps	22 max steps	7.43 avg steps	25 max steps	39,628 final numbers
72	260,887,834,350	366 fixed pts	27,378 cycles	7 nodes	4.81 avg steps	60 max steps	7.79 avg steps	63 max steps	81,437 final numbers
73	293,052,087,900	265 fixed pts	15,479 cycles	5 nodes	4.44 avg steps	23 max steps	7.44 avg steps	27 max steps	45,952 final numbers
74	328,693,558,050	396 fixed pts	31,087 cycles	7 nodes	4.74 avg steps	61 max steps	7.72 avg steps	64 max steps	92,507 final numbers
75	368,136,785,016	287 fixed pts	17,862 cycles	5 nodes	4.46 avg steps	26 max steps	7.42 avg steps	27 max steps	53,057 final numbers
76	411,731,930,610	425 fixed pts	35,188 cycles	7 nodes	4.67 avg steps	63 max steps	7.68 avg steps	66 max steps	104,756 final numbers
77	459,856,441,980	313 fixed pts	20,530 cycles	5 nodes	4.42 avg steps	23 max steps	7.40 avg steps	26 max steps	61,010 final numbers
78	512,916,800,670	457 fixed pts	39,712 cycles	7 nodes	4.62 avg steps	64 max steps	7.64 avg steps	67 max steps	118,269 final numbers
79	571,350,360,240	339 fixed pts	23,512 cycles	5 nodes	4.37 avg steps	23 max steps	7.35 avg steps	26 max steps	69,899 final numbers