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%I #8 Dec 12 2013 12:16:48
%S 1,1,2,4,8,13,23,39,67,113,191,324,548,928,1570,2657,4495,7603,12862,
%T 21758,36806,62262,105322,178163,301381,509814,862400,1458832,2467754,
%U 4174442,7061468,11945147,20206356,34180980,57820390,97808707,165452761,279879132,473442259,800872756
%N The continued fraction of the positive constant r < sqrt(3) such that the partial quotients equal the integer floor of the powers of r.
%e This constant r, found in the interval (1, sqrt(3)), satisfies the continued fraction:
%e r = [1; [r], [r^2], [r^3], [r^4], ..., floor(r^n), ...], more explicitly:
%e r = [1; 1, 2, 4, 8, 13, 23, 39, 67, 113, 191, 324, 548, 928, ...] where
%e r = 1.691595419636107091520608953850126286827042452195819302381...
%e See A227233 for another constant that satisfies a continued fraction of the same construction but is found in the interval (sqrt(3), 2).
%o (PARI) {a(n)=local(r=sqrt(3)-1/10^4);for(i=1,10,M=contfracpnqn(vector(2*n+2,k,floor(r^(k-1))));r=M[1,1]/M[2,1]*1.);floor(r^n)}
%o for(n=0,40,print1(a(n),", "))
%Y Cf. A227233.
%K nonn,cofr
%O 0,3
%A _Paul D. Hanna_, Jul 03 2013
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