A199793 - OEIS

%I #10 Feb 08 2025 22:36:14

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

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

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

%N Decimal expansion of x > 0 satisfying 3*x^2 - 2*x*cos(x) = sin(x).

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

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

%e 0.77644310890383810190966994916298288791800514780...

%t a = 3; b = -2; c = 1;

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199793 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 10 2011

%E a(96) onwards corrected by _Georg Fischer_, Aug 03 2021