“3x+1问题”轨迹
|
A编号
|
弹道 直到知道为止
|
弹道 直到1
|
步骤 到1 (A127933号)
|
1
|
琐碎的循环
|
{1, 4, 2, 1, ...} |
{1, ...} |
0 |
三
|
A033478号
|
{3, 10, 5, 16, 8, 4, 2, 1, ...} |
{3, 10, 5, 16, 8, 4, 2, 1, ...} |
7 |
6
|
— |
{6, 3, ...} |
{6, 3, 10, 5, 16, 8, 4, 2, 1, ...} |
8 |
7
|
— |
{7、22、11、34、17、52、26、13、40、20、10…}(见n=3) |
{7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
16 |
9
|
— |
{9, 28, 14, 7, ...} |
{9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
19 |
12
|
— |
{12, 6, ...} |
{12, 6, 3, 10, 5, 16, 8, 4, 2, 1, ...} |
9 |
15
|
— |
{15、46、23、70、35、106、53、160、80、40…}(参见n=7) |
{15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
17 |
18
|
— |
{18, 9, ...} |
{18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
20 |
19
|
— |
{19、58、29、88、44、22…}(参见n=9) |
{19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
20 |
21
|
A033481号
|
{21、64、32、16…}(参见n=3) |
{21, 64, 32, 16, 8, 4, 2, 1, ...} |
7 |
24
|
— |
{24, 12, ...} |
{24, 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, ...} |
10 |
25
|
— |
{25, 76, 38, 19, ...} |
{25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
23 |
27
|
A008884号
|
{27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, ...} (见n=15) |
{27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
111 |
30
|
— |
{30, 15, ...} |
{30, 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
18 |
33
|
A008880型
|
{33, 100, 50, 25...} |
{33, 100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
26 |
36
|
— |
{36, 18, ...} |
{36, 18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
21 |
37
|
— |
{37, 112, 56, 28, 14, 7, ...} |
{37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
21 |
39
|
A008878号
|
{39、118、59、178、89、268、134、67、202、101、304、152、76…}(参见n=25) |
{39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
34 |
42
|
— |
{42, 21, ...} |
{42, 21, 64, 32, 16, 8, 4, 2, 1, ...} |
8 |
43
|
— |
{43, 130, 65, 196, 98, 49, 148, 74, 37, ...} |
{43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
29 |
45
|
— |
{45、136、68、34…}(参见n=7) |
{45, 136, 68, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
16 |
48
|
— |
{48, 24, ...} |
{48, 24, 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, ...} |
11 |
51
|
A008883号
|
{51、154、77、232、116、58…}(参见n=19) |
{51, 154, 77, 232, 116, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
24 |
54
|
— |
{54, 27, ...} |
{54, 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
112 |
55
|
A008873号
(n=97)
|
{55、166、83、250、125、376、188、94…}(参见n=27) |
{55, 166, 83, 250, 125, 376, 188, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
112 |
57
|
A008877号
|
{57, 172, 86, 43, ...} |
{57, 172, 86, 43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
32 |
60
|
— |
{60, 30, ...} |
{60, 30, 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...} |
19 |
“3x+1问题”减少轨迹
|
A编号
|
减少的轨迹 直到知道为止
|
减少的轨迹 直到1
|
步骤 到1 (答:)
|
1
|
琐碎的循环
|
{1, ...} |
{1, ...} |
0 |
三
|
— |
{3, 5, 1, ...} |
{3, 5, 1, ...} |
2 |
5
|
— |
{5, 1, ...} |
{5, 1, ...} |
1 |
7
|
— |
{7, 11, 17, 13, 5, ...} |
{7, 11, 17, 13, 5, 1, ...} |
5 |
9
|
— |
{9, 7, ...} |
{9, 7, 11, 17, 13, 5, 1, ...} |
6 |
11
|
— |
{11, 17, 13, 5, ...} |
{11, 17, 13, 5, 1, ...} |
4 |
13
|
— |
{13, 5, ...} |
{13, 5, 1, ...} |
2 |
15
|
— |
{15, 23, 35, 53, 5, ...} |
{15, 23, 35, 53, 5, 1, ...} |
5 |
17
|
— |
{17, 13, ...} |
{17, 13, 5, 1, ...} |
三 |
19
|
— |
{19, 29, 11, ...} |
{19, 29, 11, 17, 13, 5, 1, ...} |
6 |
21
|
— |
{21, 1, ...} |
{21, 1, ...} |
1 |
23
|
— |
{23, 35, 53, 5, ...} |
{23, 35, 53, 5, 1, ...} |
4 |
25
|
— |
{25, 19, ...} |
{25, 19, 29, 11, 17, 13, 5, 1, ...} |
7 |
27
|
— |
{27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, ...} |
{27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
41 |
29
|
— |
{29, 11, ...} |
{29, 11, 17, 13, 5, 1, ...} |
5 |
31
|
— |
{31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, ...} |
{31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
39 |
33
|
— |
{33, 25...} |
{33, 25, 19, 29, 11, 17, 13, 5, 1, ...} |
8 |
35
|
— |
{35, 53, 27, ...} |
{35, 53, 27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
43 |
37
|
— |
{37, 7, ...} |
{37, 7, 11, 17, 13, 5, 1, ...} |
6 |
39
|
— |
{39, 59, 89, 67, 101, 19, ...} |
{39, 59, 89, 67, 101, 19, 29, 11, 17, 13, 5, 1, ...} |
11 |
41
|
— |
{41, 31, ...} |
{41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
40 |
43
|
— |
{43, 65, 49, 37, ...} |
{43, 65, 49, 37, 7, 11, 17, 13, 5, 1, ...} |
9 |
45
|
— |
{45, 17, ...} |
{45, 17, 13, 5, 1, ...} |
4 |
47
|
— |
{47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, ...} |
{47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
38 |
49
|
— |
{49, 37, ...} |
{49, 37, 7, 11, 17, 13, 5, 1, ...} |
7 |
51
|
— |
{51, 77, 29, ...} |
{51, 77, 29, 11, 17, 13, 5, 1, ...} |
7 |
53
|
— |
{53, 27, ...} |
{53, 27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
42 |
55
|
— |
{55, 83, 125, 47, ...} |
{55, 83, 125, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, ...} |
41 |
57
|
— |
{57, 43, ...} |
{57, 43, 65, 49, 37, 7, 11, 17, 13, 5, 1, ...} |
10 |
59
|
— |
{59, 89, 67, 101, 19, ...} |
{59, 89, 67, 101, 19, 29, 11, 17, 13, 5, 1, ...} |
10 |