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Decimal expansion of least x > 0 satisfying x^2 + 4*x + 1 = tan(x).
2

%I #14 Aug 05 2018 08:25:34

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

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

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

%N Decimal expansion of least x > 0 satisfying x^2 + 4*x + 1 = tan(x).

%C See A200338 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200354/b200354.txt">Table of n, a(n) for n = 1..10000</a>

%e 1.45977234643857003377170287358954477353...

%t a = 1; b = 4; c = 1;

%t f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]

%t Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200354 *)

%o (PARI) solve(x=1, 3/2, x^2 + 4*x + 1 - tan(x)) \\ _Michel Marcus_, Aug 05 2018

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 17 2011