分数化小数，小数部分出现2021，求分母最小值

王守恩

王守恩 发表于 2022-4-23 09:08
\(\pi\) 的连分数。《整数序列在线百科全书(OEIS)》A002486       
7, 106, 113, 33102, 33215, 66317, 99532, ...

谢谢 uk702!

\(\pi \)的连分数
7, 106, 113, 33102, 33215, 66317, 99532, 265381, 364913, 1360120,
1725033, 25510582, 52746197, 78256779, 131002976, 340262731,...

\(\pi\) 的误差分数\((\frac{1}{10})^k\)
5, 7, 64, 106, 113, 113, 24175, 32085, 33102, 99532, 265381, 1360120,
1725033, 18610450, 25510582, 78256779, 340262731, 811528438, ........

\(\pi\) 的误差分数\((\frac{1}{5})^k\)
7, 22, 50, 92, 113, 784, 3157, 11406, 24062, 30842, 32763, 33102, 66317,
165849, 630294, 995207, 3085153,  8260252,  18610450,  25510582, ..........

\(\pi \)的误差分数\((\frac{1}{\pi})^k\)
7, 8, 15, 36, 64, 92, 106, 332, 897, 2479, 6660, 14570, 23610, 29373, 31859,
32763, 33102, 66317, 165849, 265381, 630294, 995207, 3085153, 4810186, ....

\(\pi\) 的误差分数\((\frac{1}{e})^k\)
7, 8, 8, 22, 43, 71, 92, 106, 219, 558, 1462, 3609, 8129, 15474, 23384, 28808,
31407, 32537, 32989, 33102, 66317, 165849, 165849, 265381, 630294, 995207, .....


\(\pi \)的误差分数\((\frac{1}{2})^k\)
7, 7, 8, 8, 8, 15, 22, 29, 50, 64, 85, 99, 106, 219, 332, 671, 1123, 2253, 4174, 7338,
11971, 17621, 22932, 27226, 29938, 31520, 32311, 32763, 32989, 33102, 66317, ......