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Records in the continued fraction expansion A100864.
4

%I #16 Apr 25 2022 16:58:46

%S 1,4,74,8457,186282390,430917181166219,41151315877490090952542206046,

%T 13991468824374967392702752173757116934238293984253807017

%N Records in the continued fraction expansion A100864.

%C These terms are doubly exponential. The next term has 106 digits. Positions of these large partial quotients are given by A100866. _Hans Havermann_ has observed that the ratio of number-of-digits to position number is about 1.03, nearly equal to the reciprocal of Lochs constant.

%H Dzmitry Badziahin and Jeffrey Shallit, <a href="http://arxiv.org/abs/1505.00667">An Unusual Continued Fraction</a>, arXiv:1505.00667 [math.NT], 2015.

%H Dzmitry Badziahin and Jeffrey Shallit, <a href="https://doi.org/10.1090/proc/12848">An unusual continued fraction</a>, Proc. Amer. Math. Soc. 144 (2016), 1887-1896.

%Y Cf. A006519, A100338, A100863, A100864, A100866.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Nov 21 2004