|
%I #10 Aug 03 2021 14:27:51
%S 1,2,9,4,7,7,1,7,6,5,5,1,0,2,7,0,5,4,1,9,0,0,6,8,1,0,3,1,4,7,0,2,1,8,
%T 5,6,1,4,4,2,6,6,2,1,5,3,7,0,6,5,4,5,4,3,4,4,6,0,7,2,0,1,7,0,6,5,9,4,
%U 4,5,0,0,9,8,6,3,5,1,4,4,3,2,5,3,4,0,2,1,4,0,8,1,8,5,8,4,8,8,0
%N Decimal expansion of x < 0 satisfying 2*x^2 + x*cos(x) = 3.
%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -1.29477176551027054190068103147021856144266...
%e positive: 1.120827899072464105010802655123824414841540...
%t a = 2; b = 1; c = 3;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199267 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.12, 1.13}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199268 *)
%Y Cf. A199170, A199268.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 04 2011
%E a(93) onwards corrected by _Georg Fischer_, Aug 03 2021
|
