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%I #6 Mar 30 2012 18:57:50
%S 1,7,7,0,8,2,3,2,3,7,2,1,8,8,5,5,8,9,9,1,2,2,0,5,2,6,6,6,0,8,4,8,0,1,
%T 0,6,0,3,9,7,2,3,1,3,7,4,3,0,6,9,2,7,8,5,0,8,0,4,1,8,7,4,2,7,9,4,9,6,
%U 8,8,4,9,0,1,8,2,3,4,3,0,7,8,8,1,4,2,9,4,3,2,8,2,9,0,8,8,4,4,1,7
%N Decimal expansion of the least x>0 satisfying 1=x*cos(3*x).
%e x=1.770823237218855899122052666084801060397231374306...
%t Plot[{1/x, Cos[x], Cos[2 x], Cos[3 x], Cos[4 x]}, {x, 0, 2 Pi}]
%t t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
%t RealDigits[t] (* A133868 *)
%t t = x /. FindRoot[1/x == Cos[2 x], {x, 2, 3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196608 *)
%t t = x /. FindRoot[1/x == Cos[3 x], {x, 1, 2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196602 *)
%t t = x /. FindRoot[1/x == Cos[4 x], {x, .9, 1.4}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196609 *)
%t t = x /. FindRoot[1/x == Cos[5 x], {x, .9, 1.2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196626 *)
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 05 2011
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