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常數數字掃描


掃描一個常數的十進位制展開(包括小數點左側的任何數字),直到所有 n-位字串都出現過(包括 0 填充的字串)。下表給出了為了遇到所有 n=1, 2, ...-位字串必須掃描的位數(其中“位數”指的是 n-位字串的結尾數字,而不是起始數字),以及最後遇到的 n-位字串。

常數OEIS序列
Apéry 常數A03690623, 457, 7839, 83054, 1256587, 13881136, 166670757, ...
A0369027, 89, 211, 2861, 43983, 29270, 8261623, ...
Catalan 常數A00000032, 716, 7700, 86482, 1143572, ...
A0000008, 45, 529, 2679, 24200, ...
Champernowne 常數A07229011, 192, 2893, 38894, 488895, 5888896, 68888897, 788888898, 8888888899, ...
Copeland-Erdős 常數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, ...
尤拉-馬歇羅尼常數A00000016, 658, 6600, 91101, 1384372, ...
A0000008, 18, 346, 2778, 84514, ...
格萊舍-金克林常數A00000022, 495, 7233, ...
A0000005, 98, 478, ...
黃金比例A00000023, 770, 5819, 93910, 1154766, 13192647, ...
A0000005, 55, 515, 0092, 67799, 290503, ...
Golomb-Dickman 常數A00000028, 587, 6322, ...
A0000001, 33, 821, ...
辛欽常數A00000023, 499, 8254, ...
A0000007, 43, 782, ...
自然對數 2A03690522, 444, 7655, 98370, 1107795, 12983306, ...
A0369012, 98, 604, 1155, 46847, 175403, ...
自然對數 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, ...
畢達哥拉斯常數A00000019, 420, 8326, 94388, 1256460, 13043524, ...
A0000008, 81, 748, 8505, 30103, 489568, ...
索爾德納常數A00000034, 512, 7454, 92508, ...
A0000007, 46, 102, 5858, ...
特奧多魯斯常數A00000023, 378, 7862, 77437, 1237533, 16362668, ...
A0000004, 91, 184, 5566, 86134, 35343, ...

下表總結了常數的十進位制展開中 n=0, 1, 2, ... 首次出現的起始位置,其中小數點左側的任何初始 0 都將被忽略,任何非零初始數字都將被視為“第一”位數字。

常數OEIS0, 1, 2, ... 的首次出現
Apéry 常數A2291873, 1, 2, 10, 16, 6, 7, 23, 18, 8, ...
Catalan 常數A10007916, 2, 13, 24, 9, 3, 5, 11, 32, 1, ...
Champernowne 常數A22918611, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
Copeland-Erdős 常數A22919048, 5, 1, 2, 21, 3, 31, 4, 41, 12, ...
eA08857614, 3, 1, 18, 11, 12, 21, 2, 4, 13, ...
尤拉-馬歇羅尼常數A22919211, 5, 4, 14, 9, 1, 7, 2, 16, 10, 36, ...
格萊舍-金克林常數A22919312, 1, 2, 18, 5, 22, 14, 7, 3, 10, 11, ...
Golomb-Dickman 常數A22919515, 28, 2, 4, 3, 10, 1, 17, 8, 6, 28, ...
黃金比例A0885775, 1, 20, 6, 12, 23, 2, 11, 4, 8, 232, ...
辛欽常數A2291968, 10, 1, 14, 5, 4, 2, 23, 3, 22, 10, ...
自然對數 2A1000779, 4, 22, 3, 5, 10, 1, 6, 8, 2, 108, ...
自然對數 10A2291973, 21, 1, 2, 13, 5, 17, 22, 6, 9, 41, ...
πA03244533, 2, 7, 1, 3, 5, 8, 14, 12, 6, 50, ...
畢達哥拉斯常數A22919914, 1, 5, 7, 2, 8, 9, 12, 19, 15, 77, ...
索爾德納常數A22920117, 1, 8, 5, 2, 3, 6, 34, 11, 7, 16, ...
特奧多魯斯常數A2292005, 1, 4, 3, 23, 6, 12, 2, 8, 18, 48, ...

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常數, 常數素數

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參考文獻

Sloane, N. J. A. “整數數列線上百科全書”中的數列 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

請引用為

Weisstein, Eric W. “常數數字掃描”。來自 Web 資源。 https://mathworld.tw/ConstantDigitScanning.html

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