A200353 - OEIS

%I #15 Feb 07 2025 16:44:06

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

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

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

%N Decimal expansion of least x > 0 satisfying x^2 + 3*x + 4 = tan(x).

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

%H G. C. Greubel, <a href="/A200353/b200353.txt">Table of n, a(n) for n = 1..10000</a>

%e 1.4768369420356295966002253324996856643...

%t a = 1; b = 3; c = 4;

%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]   (* A200353 *)

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

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 17 2011

%E Terms a(90) onward corrected by _G. C. Greubel_, Aug 04 2018