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%I #6 Nov 03 2016 06:23:27
%S 1,1,1,3,7,37,1033,467757,33820512481,30277741778897513797,
%T 785696122254571911501384128129833729,
%U 1350037852944002174045556752948635277284099036085244331545069453543
%N Numerators of fractions converging to square root 3 satisfying: a(n)=1/a(n-1)+1/a(n-2)+ 1/a(n-3) or denominators of reciprocal satisfying: a(n)=1/(a(n-1)+ a(n-2)+ a(n-3)) with a(1,2,3)= 1
%C For other square roots of positive integers add or subtract more a(n)to formula and start off.
%e For n=5 a(5)= 1/1 + 1/1 + 1/3 = 7/3 (numerator)
%e For n=5 a(5)= 1/(1 + 1 + 1/3) = 3/7 (denominator)
%e Convergents are 1, 1, 1, 3, 2.3333.., 1.7619047...., 1.748317..., 1.89172..., 1.852777..., 1.64032..., 1.677983... - _R. J. Mathar_, Nov 03 2016
%Y Cf. A162924 (denominators), A002194, A057677, A066932.
%K nonn,frac
%O 1,4
%A _Mark Dols_, Jul 17 2009
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