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%I #7 Mar 30 2012 18:57:50
%S 4,9,2,9,1,2,4,5,1,7,5,4,9,0,7,5,7,4,1,8,7,7,8,0,1,8,9,8,2,2,2,3,2,9,
%T 7,6,9,1,5,6,9,7,0,1,3,2,5,7,1,1,5,0,0,7,0,2,5,9,2,6,5,3,6,0,0,4,0,4,
%U 4,9,2,5,9,1,0,6,8,6,4,1,8,3,4,8,9,2,0,2,5,0,0,7,1,0,6,4,7,4,5,9
%N Decimal expansion of greatest x>0 satisfying sin(1/x)=1/sqrt(1+x^2).
%C Let M be the greatest x>0 satisfying sin(1/x)=1/sqrt(1+x^2). Then sin(1/x) > 1/sqrt(1+x^2) for all x>M=0.4929... See A196500-A196504 for related constants and inequalities.
%e x=0.4929124517549075741877801898222329769156970132...
%t Plot[{Sin[x], x/Sqrt[1 + x^2]}, {x, 0, 9}]
%t Plot[{Sin[1/x], 1/Sqrt[1 + x^2]}, {x, 0.1, 1.0}] (for A196505)
%t t = x /.FindRoot[Sin[x] == x/Sqrt[1 + x^2], {x, .10, 3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196504 *)
%t 1/t
%t RealDigits[1/t] (* A196505 *)
%Y Cf. A196500, A196502, A196503.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 03 2011
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