A196405 - OEIS

%I #8 Aug 09 2021 13:43:54

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

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

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

%N Decimal expansion of the least positive number x satisfying e^(-x)=5*cos(x).

%e x=1.52736110301540629047060641021913565224700...

%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