2024-11-16
前回の記事で数列が一致する初期値を見つけた。
| 数列が一致する初期値のペア | 数列 |
|---|---|
| 1 と 5 | 1 |
| 3 と 13 | 5, 1 |
| 5 と 21 | 1 |
| 7 と 29 | 11, 17, 13, 5, 1 |
| 9 と 37 | 7, 11, 17, 13, 5, 1 |
| 11 と 45 | 17, 13, 5, 1 |
| 13 と 53 | 5, 1 |
| 15 と 61 | 23, 35, 53, 5, 1 |
この点について、react-katex を記事のレンダリングにうまく実装できなかったため別のページにメモした（バックエンドで katex 実装したほうがよいかもしれない）。
https://oizumi-yuta.com/collatz/memo
このことから奇数の初期値（偶数の初期値は考慮不要）a を 4 倍して 1 を足した初期値 b は a と同じ数列になるため、b を調べる必要がない。よって 4n + 1 型（n は奇数）の初期値は除外してよい（8n + 5 型の初期値に等しい）。
| 初期値 | 数列 |
|---|---|
| 1 | 1 |
| 3 | 5, 1 |
| 7 | 11, 17, 13, 5, 1 |
| 9 | 7, 11, 17, 13, 5, 1 |
| 11 | 17, 13, 5, 1 |
| 15 | 23, 35, 53, 5, 1 |
| 17 | 13, 5, 1 |
| 19 | 29, 11, 17, 13, 5, 1 |
| 23 | 35, 53, 5, 1 |
| 25 | 19, 29, 11, 17, 13, 5, 1 |
| 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 |
| 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 |
| 33 | 25, 19, 29, 11, 17, 13, 5, 1 |
| 35 | 53, 5, 1 |
| 39 | 59, 89, 67, 101, 19, 29, 11, 17, 13, 5, 1 |
| 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 | 65, 49, 37, 7, 11, 17, 13, 5, 1 |
| 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 |
| 49 | 37, 7, 11, 17, 13, 5, 1 |
| 51 | 77, 29, 11, 17, 13, 5, 1 |
| 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 |
| 57 | 43, 65, 49, 37, 7, 11, 17, 13, 5, 1 |
| 59 | 89, 67, 101, 19, 29, 11, 17, 13, 5, 1 |
| 63 | 95, 143, 215, 323, 485, 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 |
| 65 | 49, 37, 7, 11, 17, 13, 5, 1 |
| 67 | 101, 19, 29, 11, 17, 13, 5, 1 |
| 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 |
| 73 | 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 |
| 75 | 113, 85, 1 |
| 79 | 119, 179, 269, 101, 19, 29, 11, 17, 13, 5, 1 |
| 81 | 61, 23, 35, 53, 5, 1 |
| 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 |
| 87 | 131, 197, 37, 7, 11, 17, 13, 5, 1 |
| 89 | 67, 101, 19, 29, 11, 17, 13, 5, 1 |
| 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 |
| 95 | 143, 215, 323, 485, 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 |
| 97 | 73, 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 |
| 99 | 149, 7, 11, 17, 13, 5, 1 |