A199621 - OEIS

%I #10 Feb 07 2025 19:51:30

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

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

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

%N Decimal expansion of x<0 satisfying 2*x+cos(x)=0.

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%C This is the abscissa point x = 0.45018... where a parabola y=x^2+a and the curve y=sin(x) touch at exactly one point, a=0.23246557... - _R. J. Mathar_, Aug 27 2024

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e -0.450183611294873573036538696762681827320...

%t a = 2; b = 1; c = 0;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -.46, -.45}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199621 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 08 2011