A198607 - OEIS

%I #13 Dec 27 2017 01:42:04

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

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

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

%N Decimal expansion of x < 0 satisfying 3*x^2 + 4*x = 2*sin(x).

%C See A198414 for a guide to related sequences.  The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A198607/b198607.txt">Table of n, a(n) for n = 0..10000</a>

%e x = -0.723293071335853335535036493209789739274570...

%t a = 3; b = 4; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -1, .1}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.73, -.72}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A198607 *)

%o (PARI) solve(x=-1, -0.5, 3*x^2 + 4*x - 2*sin(x)) \\ _Iain Fox_, Dec 26 2017

%Y Cf. A198414.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 28 2011