把二进制数看成十进制数后再转成二进制

王守恩

4 转化成四进制是 10,
10 转化成四进制是 22,
22 转化成四进制是 112,
112 转化成四进制是 1300,
1300 转化成四进制是 110110,
110110 转化成四进制是 122320132,
122320132 转化成四进制是 13102213110010,
13102213110010 转化成四进制是 2332222120300201203322,
2332222120300201203322 转化成四进制是 133212320111123130111021311111121322,
133212320111123130111021311111121322 转化成四进制是 12122133133313032110200332320320202022333020121323230212222,
......
把这些数字的位数写下来——{1, 2, 2, 3, 4, 6, 9, 14, 22, 36, 59, 97, 160, 265, 440, 730, 1211, 2011, 3340, 5546, 9211, 15299, 25410, 42204, 70099, 116431, 193387, 321208, 533514, 886147, 1471858, 2444702, 4060562, 6744446, 11202282}

把这些数字中的"3"统计一下——{0, 0, 0, 1, 0, 2, 2, 5, 7, 17, 21, 34, 76, 110, 188, 289, 464, 793, 1364, 2334, 3868, 6199, 10659, 17400, 29108, 48432, 80241, 133642, 220965, 367409, 611598, 1015280, 1687547, 2799672, 4652196, 7730260}

王守恩

2 转化成二进制是 10,
三进制 10 转化成二进制是 11,
三进制 11 转化成二进制是 100,
三进制 100 转化成二进制是 1001,
三进制 1001 转化成二进制是 11100,
三进制 11100 转化成二进制是 1110101,
三进制 1110101 转化成二进制是 10000100111,
三进制 10000100111 转化成二进制是 1110011110101001,
三进制 1110011110101001 转化成二进制是 1001111011001100001111110,
三进制 1001111011001100001111110 转化成二进制是 100010101100001010000100000101000100101,
三进制 100010101100001010000100000101000100101 转化成二进制是 1001100000001111111111000111111011010101000111001110101000111,
三进制 1001100000001111111111000111111011010101000111001110101000111 转化成二进制是 100011111011110011011010111101010001000000000010000011101001000001101001101000000001010111110101,
......
把这些数字的位数写下来——{1, 2, 2, 3, 4, 5, 7, 11, 16, 25, 39, 61, 96, 151, 239, 378, 598, 947, 1500, 2377, 3767, 5969, 9460, 14993, 23762, 37661, 59691, 94607, 149948, 237661, 376683, 597027, 946265, ——可以有50项吗？

把"1"提出来——{0, 1, 2, 1, 2, 3, 5, 5, 10, 15, 13, 35, 43, 81, 119, 202, 297, 480, 761, 1192, 1896, 2988, 4753, 7577, 11881, 18847, 29939, 47142, 74475, 118729, 188167, 299251, 472941, 749837, 1188775, 1884970, 2986334}

王守恩

学了一招。谢谢各位好友！！

{1, 2, 4, 10, 31, 100, 330, 1093, 3628, 12049, 40023, 132951, 441651, 1467130, 4873698, 16190071, 53782249, 178660761, 593498199, 1971558339, 6549375034, 21756552927, 72273704413, 240088049208, 797555235908, 2649421145384,
8801186538037, 29236908829047, 97122908846869, 322635319555596, 1071771332434694, 3560347300509670, 11827217725119449, 39289166845424092, 130515787168531371, 433564060221483867, 1440268632583183540,
4784468834763081346, 15893661441312481253, 52797600472523900437, 175389832352315422663, 582632411648741041920, 1935462977247931791628, 6429468840734244393709, 21358233177237966605394, 70950514848622174528405,
235692508622360974195958, 782953566147102814617343, 2600915448376311691313555, 8640054100387830930358540, 28701638457425090555526915, 95344779161019984506204705, 316728500595823403320105922,
1052149304580814448477908456, 3495164334903208087022834978, 11610684600363268945421466506, 38569859374822790062833434036, 128126299473078543553061211470, 425626353913571464421883265664,
1413900142989964696264005783930, 4696874608363622635125333090739, 15602679719686195079367186445692, 51830980116354846807243775876948, 172178789034067414690517780784713, 571965556635952642441117800893573}

1. p = 4000;(*提高精度*)v = N[Log[2, 10], p]; x = N[1, p]; w = {1};(*第0项*)
   
2. Do[B = IntegerPart[x] + 1;(*当前项位数*)AppendTo[w, B];
   
3. b = RealDigits[2^FractionalPart[x], 2, p + 20][[1]];
   
4. s = FromDigits[b]/10^(Length[b] - 1);(*十进制有效数字*)
   
5. x = v (B - 1) + Log[2, s]; x = N[x, p], {k, 64}(*这里想要多少项就填多少*)]; w

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补充内容 (2026-5-2 08:50):
p=4000改p=313,p+20改p+0就可以有{k, 601}。——312不行。

王守恩

接22#。
2 转化成二进制是 10,
三进制 10 转化成二进制是 11,
三进制 11 转化成二进制是 100,
三进制 100 转化成二进制是 1001,
三进制 1001 转化成二进制是 11100,
三进制 11100 转化成二进制是 1110101,
三进制 1110101 转化成二进制是 10000100111,
三进制 10000100111 转化成二进制是 1110011110101001,
三进制 1110011110101001 转化成二进制是 1001111011001100001111110,
三进制 1001111011001100001111110 转化成二进制是 100010101100001010000100000101000100101,
三进制 100010101100001010000100000101000100101 转化成二进制是 1001100000001111111111000111111011010101000111001110101000111,
三进制 1001100000001111111111000111111011010101000111001110101000111 转化成二进制是 100011111011110011011010111101010001000000000010000011101001000001101001101000000001010111110101,
......
把这些数字的位数写下来——{1, 2, 2, 3, 4, 5, 7, 11, 16, 25, 39, 61, 96, 151, 239, 378, 598, 947, 1500, 2377, 3767, 5969, 9460, 14993, 23762, 37661, 59691, 94607, 149948, 237661, 376683, 597027, 946265, 1499794, 2377116, 3767639, \
5971566, 9464707, 15001205, 23776347, 37684617, 59728704, 94667755, 150044841, 237815446, 376928563, 597417637, 946884551, 1500776505, 2378674482, 3770109854, 5975482742, 9470916069, 15011046816, 23791946299,
37709342702, 59767894109, 94729870909, 150143293088, 237971489278, 377175886746, 597809636668, 947505856687, 1501761252062, 2380235269553, 3772583645135, 5979403608372, 9477130495946, 15020896450514, 23807557601280,
37734086031787, 59807111359367, 94792028781050, 150241810985244, 238127636452047, 377423374161854, 598201894942188, 948127571343704, 1502746646479592, 2381797082754625, 3775059060493124, 5983327048889240, \
9483349002040024, 15030752549484837, 23823179148552380, 37758845598417684, 59846354344012112, 94854227440129865, 150340393527481543, 238283886084719868, 377671023970392711, 598594410602033350, 948749693945505342,
1503732687474299716, 2383359920755410886, 3777536100119072665, 5987253063809169217, 9489571588465384921, 15040615115626530858, 23838810946047847977, \37783621411266868121}

1. p = 2000;(*提高精度*)V = N[Log[2, 3], p]; x = N[1, p]; W = {1};(*第0项*)
   
2. Do[B = Floor[x] + 1;(*当前项位数*)AppendTo[W, B];
   
3. b = RealDigits[2^FractionalPart[x], 2, p][[1]];
   
4. s = 1 + FromDigits[Rest[b], 3]/3^Length[Rest[b]];(*三进制小数+1*)
   
5. x = V (B - 1) + Log[2, s]; x = N[x, p], {k, 100}(*这里想要多少项就填多少*)];W

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题外话。这帖子蛮好的, 会有人慕名跑过来,  就想让客人带点什么回去。