Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Mar 30 2012 18:57:54
%S 6,9,6,5,8,5,8,4,7,7,7,9,0,6,5,8,0,1,9,8,6,5,9,2,4,3,4,6,3,2,7,5,4,3,
%T 5,8,8,5,5,9,0,0,5,4,6,0,3,5,9,3,5,5,5,7,7,8,4,6,5,4,9,7,8,7,6,5,8,8,
%U 3,8,9,3,3,9,9,4,9,1,0,8,6,8,4,8,8,2,3,0,7,8,6,1,8,6,4,0,5,7,1
%N Decimal expansion of least x having x^2-4x=-3*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: 0.69658584777906580198659243463275435885...
%e greatest x: 4.28804762370313657874580002787893697...
%t a = 1; b = -4; c = -3;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 5}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, 0.69, 0.70}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198144 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 4.28, 4.29}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198145 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 21 2011