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Decimal expansion of the least positive number x satisfying e^(-x)=4*cos(x).
6

%I #6 Mar 30 2012 18:57:50

%S 1,5,1,5,8,6,4,1,2,2,8,0,5,0,0,9,8,4,9,9,3,0,9,1,2,2,5,5,8,1,5,7,1,1,

%T 1,9,3,5,2,0,0,2,2,4,9,6,1,6,8,6,3,4,3,4,6,2,9,0,0,4,0,6,7,1,3,2,4,0,

%U 0,6,0,2,9,6,7,6,7,4,5,5,9,8,9,0,6,8,1,0,4,9,0,0,9,9,5,0,3,9,7,6

%N Decimal expansion of the least positive number x satisfying e^(-x)=4*cos(x).

%e x=1.515864122805009849930912255815711193520022496168...

%t Plot[{E^(-x), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, Pi/2}]

%t t = x /. FindRoot[E^(-x) == Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100];

%t RealDigits[t] (* A196401 *)

%t t = x /. FindRoot[E^(-x) == 2 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t] (* A196402 *)

%t t = x /. FindRoot[E^(-x) == 3 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t] (* A196403 *)

%t t = x /. FindRoot[E^(-x) == 4 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t] (* A196404 *)

%t t = x /. FindRoot[E^(-x) == 5 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t] (* A196405 *)

%t t = x /. FindRoot[E^(-x) == 6 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t] (* A196406 *)

%Y Cf. A196401.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 02 2011