优美的数字(1)

王守恩

优美的数字(1)、优美的数字(2)

ccmmjj

有这种规律吗？哪本书的结论？还是自已的结果？有无验算过？

王守恩

ccmmjj 发表于 2016-5-17 17:42
有这种规律吗？哪本书的结论？还是自已的结果？有无验算过？

本人所有的帖子均为自己的，别人是没有的。肯定验算过，也是正确的。

ccmmjj

对连分数展式我不太了解，但级数展开我还是略知一二的。你那Ln2的展式应该是级数展开式，不象是连分数展式。

王守恩

“数字串”是没有问题的(悬着的心总算下来了)。详见1楼 优美的数字(1)

{{1, 01, 1, 1, 05, 1, 1, 09, 1, 1, 13, 1, 1, 17, 1, 1, 021, 1, 1, 025, 1, 1, 029, 1, 1, 033, 1, 1, 037}},
{{1, 02, 1, 1, 08, 1, 1, 14, 1, 1, 20, 1, 1, 26, 1, 1, 032, 1, 1, 038, 1, 1, 044, 1, 1, 050, 1, 1, 056}},
{{1, 03, 1, 1, 11, 1, 1, 19, 1, 1, 27, 1, 1, 35, 1, 1, 043, 1, 1, 051, 1, 1, 059, 1, 1, 067, 1, 1, 075}},
{{1, 04, 1, 1, 14, 1, 1, 24, 1, 1, 34, 1, 1, 44, 1, 1, 054, 1, 1, 064, 1, 1, 074, 1, 1, 084, 1, 1, 094}},
{{1, 05, 1, 1, 17, 1, 1, 29, 1, 1, 41, 1, 1, 53, 1, 1, 065, 1, 1, 077, 1, 1, 089, 1, 1, 101, 1, 1, 113}},
{{1, 06, 1, 1, 20, 1, 1, 34, 1, 1, 48, 1, 1, 62, 1, 1, 076, 1, 1, 090, 1, 1, 104, 1, 1, 118, 1, 1, 132}},
{{1, 07, 1, 1, 23, 1, 1, 39, 1, 1, 55, 1, 1, 71, 1, 1, 087, 1, 1, 103, 1, 1, 119, 1, 1, 135, 1, 1, 151}},
{{1, 08, 1, 1, 26, 1, 1, 44, 1, 1, 62, 1, 1, 80, 1, 1, 098, 1, 1, 116, 1, 1, 134, 1, 1, 152, 1, 1, 170}},
{{1, 09, 1, 1, 29, 1, 1, 49, 1, 1, 69, 1, 1, 89, 1, 1, 109, 1, 1, 129, 1, 1, 149, 1, 1, 169, 1, 1, 189}},
{{1, 10, 1, 1, 32, 1, 1, 54, 1, 1, 76, 1, 1, 98, 1, 1, 120, 1, 1, 142, 1, 1, 164, 1, 1, 186, 1, 1, 208}}}

Table[ContinuedFraction[Power[E, (a)^-1], n], {a, 2, 11}, {n, 29, 29}]

各位网友！我们可有“方法”把这些“1”删掉？谢谢！

王守恩

这串数也是蛮好的。 ContinuedFraction[Coth[1], 41]

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, ......

王守恩

优美的数字(1)。

{1, 0, 1, 1, 02, 1, 1, 04, 1, 1, 06, 1, 1, 08, 1, 1, 010, 1, 1, 012, 1, 1, 014, 1, 1, 016, 1, 1, 018, 1, 1, 020, 1, 1, 022, 1, 1, 024, 1, 1, 026, 1, 1, 028, 1, 1, 030, 1, 1, 032},
{1, 1, 1, 1, 05, 1, 1, 09, 1, 1, 13, 1, 1, 17, 1, 1, 021, 1, 1, 025, 1, 1, 029, 1, 1, 033, 1, 1, 037, 1, 1, 041, 1, 1, 045, 1, 1, 049, 1, 1, 053, 1, 1, 057, 1, 1, 061, 1, 1, 065},
{1, 2, 1, 1, 08, 1, 1, 14, 1, 1, 20, 1, 1, 26, 1, 1, 032, 1, 1, 038, 1, 1, 044, 1, 1, 050, 1, 1, 056, 1, 1, 062, 1, 1, 068, 1, 1, 074, 1, 1, 080, 1, 1, 086, 1, 1, 092, 1, 1, 098},
{1, 3, 1, 1, 11, 1, 1, 19, 1, 1, 27, 1, 1, 35, 1, 1, 043, 1, 1, 051, 1, 1, 059, 1, 1, 067, 1, 1, 075, 1, 1, 083, 1, 1, 091, 1, 1, 099, 1, 1, 107, 1, 1, 115, 1, 1, 123, 1, 1, 131},
{1, 4, 1, 1, 14, 1, 1, 24, 1, 1, 34, 1, 1, 44, 1, 1, 054, 1, 1, 064, 1, 1, 074, 1, 1, 084, 1, 1, 094, 1, 1, 104, 1, 1, 114, 1, 1, 124, 1, 1, 134, 1, 1, 144, 1, 1, 154, 1, 1, 164},
{1, 5, 1, 1, 17, 1, 1, 29, 1, 1, 41, 1, 1, 53, 1, 1, 065, 1, 1, 077, 1, 1, 089, 1, 1, 101, 1, 1, 113, 1, 1, 125, 1, 1, 137, 1, 1, 149, 1, 1, 161, 1, 1, 173, 1, 1, 185, 1, 1, 197},
{1, 6, 1, 1, 20, 1, 1, 34, 1, 1, 48, 1, 1, 62, 1, 1, 076, 1, 1, 090, 1, 1, 104, 1, 1, 118, 1, 1, 132, 1, 1, 146, 1, 1, 160, 1, 1, 174, 1, 1, 188, 1, 1, 202, 1, 1, 216, 1, 1, 230},
{1, 7, 1, 1, 23, 1, 1, 39, 1, 1, 55, 1, 1, 71, 1, 1, 087, 1, 1, 103, 1, 1, 119, 1, 1, 135, 1, 1, 151, 1, 1, 167, 1, 1, 183, 1, 1, 199, 1, 1, 215, 1, 1, 231, 1, 1, 247, 1, 1, 263},
{1, 8, 1, 1, 26, 1, 1, 44, 1, 1, 62, 1, 1, 80, 1, 1, 098, 1, 1, 116, 1, 1, 134, 1, 1, 152, 1, 1, 170, 1, 1, 188, 1, 1, 206, 1, 1, 224, 1, 1, 242, 1, 1, 260, 1, 1, 278, 1, 1, 296},
{1, 9, 1, 1, 29, 1, 1, 49, 1, 1, 69, 1, 1, 89, 1, 1, 109, 1, 1, 129, 1, 1, 149, 1, 1, 169, 1, 1, 189, 1, 1, 209, 1, 1, 229, 1, 1, 249, 1, 1, 269, 1, 1, 289, 1, 1, 309, 1, 1, 329},
......

1. Table[ContinuedFraction[Power[E, (a)^-1], 50], {a, 10}]

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这些1可以删除吗？

王守恩

谢谢 northwolves！

{0, 02, 04, 06, 08, 010, 012, 014, 016, 018, 020, 022, 024, 026, 028, 030, 032, 034, 036, 038, 040, 042, 044, 046, 048, 050, 052, 054, 056, 058, 060, 062, 064, 066, 068, 070, 072, 074, 076},
{1, 05, 09, 13, 17, 021, 025, 029, 033, 037, 041, 045, 049, 053, 057, 061, 065, 069, 073, 077, 081, 085, 089, 093, 097, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153},
{2, 08, 14, 20, 26, 032, 038, 044, 050, 056, 062, 068, 074, 080, 086, 092, 098, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 182, 188, 194, 200, 206, 212, 218, 224, 230},
{3, 11, 19, 27, 35, 043, 051, 059, 067, 075, 083, 091, 099, 107, 115, 123, 131, 139, 147, 155, 163, 171, 179, 187, 195, 203, 211, 219, 227, 235, 243, 251, 259, 267, 275, 283, 291, 299, 307},
{4, 14, 24, 34, 44, 054, 064, 074, 084, 094, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 204, 214, 224, 234, 244, 254, 264, 274, 284, 294, 304, 314, 324, 334, 344, 354, 364, 374, 384},
{5, 17, 29, 41, 53, 065, 077, 089, 101, 113, 125, 137, 149, 161, 173, 185, 197, 209, 221, 233, 245, 257, 269, 281, 293, 305, 317, 329, 341, 353, 365, 377, 389, 401, 413, 425, 437, 449, 461},
{6, 20, 34, 48, 62, 076, 090, 104, 118, 132, 146, 160, 174, 188, 202, 216, 230, 244, 258, 272, 286, 300, 314, 328, 342, 356, 370, 384, 398, 412, 426, 440, 454, 468, 482, 496, 510, 524, 538},
{7, 23, 39, 55, 71, 087, 103, 119, 135, 151, 167, 183, 199, 215, 231, 247, 263, 279, 295, 311, 327, 343, 359, 375, 391, 407, 423, 439, 455, 471, 487, 503, 519, 535, 551, 567, 583, 599, 615},
{8, 26, 44, 62, 80, 098, 116, 134, 152, 170, 188, 206, 224, 242, 260, 278, 296, 314, 332, 350, 368, 386, 404, 422, 440, 458, 476, 494, 512, 530, 548, 566, 584, 602, 620, 638, 656, 674, 692},
{9, 29, 49, 69, 89, 109, 129, 149, 169, 189, 209, 229, 249, 269, 289, 309, 329, 349, 369, 389, 409, 429, 449, 469, 489, 509, 529, 549, 569, 589, 609, 629, 649, 669, 689, 709, 729, 749, 769},

1. Table[a + 2 a (b - 1) - 1, {a, 9}, {b, 39}]

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