AN UNUSUAL CONTINUED FRACTION

作者：Badziahin Dzmitry^*; Shallit Jeffrey^*

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(5): 1887-1896.

DOI：10.1090/proc/12848

We consider the real number sigma with continued fraction expansion [a(0), a(1), a(2), ...] = [1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, ...], where a(i) is the largest power of 2 dividing i + 1. We show that the irrationality measure of sigma(2) is at least 8/3. We also show that certain partial quotients of sigma(2) grow doubly exponentially, thus confirming a conjecture of Hanna and Wilson.

• 出版日期2016-5