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%I #9 Apr 25 2022 16:58:39
%S 1,1,4,1,74,1,8457,1,186282390,1,1,1,2,1,430917181166219,11,37,1,4,2,
%T 41151315877490090952542206046,11,5,3,12,2,34,2,9,8,1,1,2,7,
%U 13991468824374967392702752173757116934238293984253807017,3,4,1,3,100,4
%N Continued fraction expansion of the square of the constant (A100338) which has the continued fraction equal to A006519 (highest power of 2 dividing n).
%C Decimal expansion is 1.832967032396... (see A100863). Records are doubly exponential and form A100865.
%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.
%o (PARI) {CFM=contfracpnqn(vector(650,n,2^valuation(n,2))); contfrac((CFM[1,1]/CFM[2,1])^2,71)}
%Y Cf. A006519, A100338, A100863, A100865.
%K cofr,nonn
%O 1,3
%A _Paul D. Hanna_, Nov 21 2004