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常数数字扫描


扫描一个常数的十进制展开(包括小数点左侧的任何数字),直到所有 n-位字符串都出现过(包括 0 填充的字符串)。下表给出了为了遇到所有 n=1, 2, ...-位字符串必须扫描的位数(其中“位数”指的是 n-位字符串的结尾数字,而不是起始数字),以及最后遇到的 n-位字符串。

常数OEIS序列
Apéry 常数A03690623, 457, 7839, 83054, 1256587, 13881136, 166670757, ...
A0369027, 89, 211, 2861, 43983, 29270, 8261623, ...
Catalan 常数A00000032, 716, 7700, 86482, 1143572, ...
A0000008, 45, 529, 2679, 24200, ...
Champernowne 常数A07229011, 192, 2893, 38894, 488895, 5888896, 68888897, 788888898, 8888888899, ...
Copeland-Erdős 常数A00000048, 934, 24437, 366399, 4910479, 49672582, ...
A0000000, 84, 504, 8580, 07010, 088880, ...
eA03690421, 372, 8092, 102128, 1061613, 12108841, 198150341, 1929504534, ...
A0369006, 12, 548, 1769, 92994, 513311, 1934715, 56891305, ...
欧拉-马歇罗尼常数A00000016, 658, 6600, 91101, 1384372, ...
A0000008, 18, 346, 2778, 84514, ...
格莱舍-金克林常数A00000022, 495, 7233, ...
A0000005, 98, 478, ...
黄金比例A00000023, 770, 5819, 93910, 1154766, 13192647, ...
A0000005, 55, 515, 0092, 67799, 290503, ...
Golomb-Dickman 常数A00000028, 587, 6322, ...
A0000001, 33, 821, ...
辛钦常数A00000023, 499, 8254, ...
A0000007, 43, 782, ...
自然对数 2A03690522, 444, 7655, 98370, 1107795, 12983306, ...
A0369012, 98, 604, 1155, 46847, 175403, ...
自然对数 10A22912422, 701, 7486, 88092, 1189434, 13426407, ...
A2291267, 38, 351, 8493, 33058, 362945, ...
πA08059733, 607, 8556, 99850, 1369565, 14118313, 166100507, 1816743913, 22445207407, 241641121049, 2512258603208, ...
A0325100, 68, 483, 6716, 33394, 569540, 1075656, 36432643, 172484538, 5918289042, 56377726040, ...
毕达哥拉斯常数A00000019, 420, 8326, 94388, 1256460, 13043524, ...
A0000008, 81, 748, 8505, 30103, 489568, ...
索尔德纳常数A00000034, 512, 7454, 92508, ...
A0000007, 46, 102, 5858, ...
特奥多鲁斯常数A00000023, 378, 7862, 77437, 1237533, 16362668, ...
A0000004, 91, 184, 5566, 86134, 35343, ...

下表总结了常数的十进制展开中 n=0, 1, 2, ... 首次出现的起始位置,其中小数点左侧的任何初始 0 都将被忽略,任何非零初始数字都将被视为“第一”位数字。

常数OEIS0, 1, 2, ... 的首次出现
Apéry 常数A2291873, 1, 2, 10, 16, 6, 7, 23, 18, 8, ...
Catalan 常数A10007916, 2, 13, 24, 9, 3, 5, 11, 32, 1, ...
Champernowne 常数A22918611, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
Copeland-Erdős 常数A22919048, 5, 1, 2, 21, 3, 31, 4, 41, 12, ...
eA08857614, 3, 1, 18, 11, 12, 21, 2, 4, 13, ...
欧拉-马歇罗尼常数A22919211, 5, 4, 14, 9, 1, 7, 2, 16, 10, 36, ...
格莱舍-金克林常数A22919312, 1, 2, 18, 5, 22, 14, 7, 3, 10, 11, ...
Golomb-Dickman 常数A22919515, 28, 2, 4, 3, 10, 1, 17, 8, 6, 28, ...
黄金比例A0885775, 1, 20, 6, 12, 23, 2, 11, 4, 8, 232, ...
辛钦常数A2291968, 10, 1, 14, 5, 4, 2, 23, 3, 22, 10, ...
自然对数 2A1000779, 4, 22, 3, 5, 10, 1, 6, 8, 2, 108, ...
自然对数 10A2291973, 21, 1, 2, 13, 5, 17, 22, 6, 9, 41, ...
πA03244533, 2, 7, 1, 3, 5, 8, 14, 12, 6, 50, ...
毕达哥拉斯常数A22919914, 1, 5, 7, 2, 8, 9, 12, 19, 15, 77, ...
索尔德纳常数A22920117, 1, 8, 5, 2, 3, 6, 34, 11, 7, 16, ...
特奥多鲁斯常数A2292005, 1, 4, 3, 23, 6, 12, 2, 8, 18, 48, ...

另请参阅

常数, 常数素数

使用 Wolfram|Alpha 探索

参考文献

Sloane, N. J. A. “整数数列在线百科全书”中的数列 A032445, A032510, A036900, A036901, A036902, A036904, A036905, A036906, A072290, A080597, A088576, A088577, A100077, A100079, A229124, A229126, A229186, A229187, A229190, A229192, A229193, A229195, A229197, A229199, A229200, 和 A229201

请引用为

Weisstein, Eric W. “常数数字扫描”。来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/ConstantDigitScanning.html

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