cp's OEIS Frontend

A199737 Decimal expansion of least x satisfying x^2-4*x*cos(x)=sin(x).

%I A199737 #8 Feb 08 2025 13:26:41
%S A199737 3,6,4,1,7,3,6,5,1,0,4,2,3,2,0,3,0,8,9,1,5,6,8,0,1,7,1,2,1,9,1,6,8,8,
%T A199737 9,1,9,4,7,4,4,1,5,6,3,0,6,1,3,8,5,4,5,6,9,0,8,9,9,4,2,4,5,1,9,9,5,8,
%U A199737 6,1,0,9,4,0,3,4,5,1,0,1,0,9,8,2,7,9,2,6,9,6,7,0,5,5,8,2,4,5,1
%N A199737 Decimal expansion of least x satisfying x^2-4*x*cos(x)=sin(x).
%C A199737 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199737 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199737 least: -3.6417365104232030891568017121916889194744...
%e A199737 greatest:  1.39694868354568477235286357946526821398...
%t A199737 a = 1; b = -4; c = 1;
%t A199737 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199737 Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
%t A199737 r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]
%t A199737 RealDigits[r]   (* A199737 least root *)
%t A199737 r = x /. FindRoot[f[x] == g[x], {x, 1.39, 1.40}, WorkingPrecision -> 110]
%t A199737 RealDigits[r]   (* A199738 greatest root *)
%Y A199737 Cf. A199597.
%K A199737 nonn,cons
%O A199737 1,1
%A A199737 _Clark Kimberling_, Nov 09 2011