cp's OEIS Frontend

A199738 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=sin(x).

%I A199738 #8 Feb 08 2025 13:26:43
%S A199738 1,3,9,6,9,4,8,6,8,3,5,4,5,6,8,4,7,7,2,3,5,2,8,6,3,5,7,9,4,6,5,2,6,8,
%T A199738 2,1,3,9,8,0,4,3,6,8,9,7,5,9,2,7,1,4,1,0,6,1,4,0,9,5,0,0,9,7,9,8,5,7,
%U A199738 9,4,3,9,4,6,9,5,5,3,7,2,4,5,5,0,3,7,8,5,0,4,7,9,5,3,7,9,7,3,8
%N A199738 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=sin(x).
%C A199738 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199738 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199738 least: -3.6417365104232030891568017121916889194744...
%e A199738 greatest:  1.39694868354568477235286357946526821398...
%t A199738 a = 1; b = -4; c = 1;
%t A199738 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199738 Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
%t A199738 r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]
%t A199738 RealDigits[r]   (* A199737 least root *)
%t A199738 r = x /. FindRoot[f[x] == g[x], {x, 1.39, 1.40}, WorkingPrecision -> 110]
%t A199738 RealDigits[r]   (* A199738 greatest root *)
%Y A199738 Cf. A199597.
%K A199738 nonn,cons
%O A199738 1,2
%A A199738 _Clark Kimberling_, Nov 09 2011