cp's OEIS Frontend

A199614 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=sin(x).

%I A199614 #8 Feb 08 2025 13:24:04
%S A199614 3,5,5,3,2,4,1,6,8,0,6,8,2,8,9,2,5,2,3,9,5,7,2,6,5,5,5,6,2,3,4,4,9,4,
%T A199614 9,0,2,0,6,7,7,6,2,6,1,8,6,1,7,2,3,9,1,5,4,2,8,6,0,0,4,2,8,8,8,6,6,0,
%U A199614 4,0,7,4,9,0,2,5,6,2,7,1,6,0,1,8,7,4,7,3,5,7,2,1,8,0,8,2,6,7,7
%N A199614 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=sin(x).
%C A199614 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199614 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199614 least: -1.077309917524072030339979615126813664791...
%e A199614 greatest:  3.553241680682892523957265556234494902...
%t A199614 a = 1; b = 4; c = 1;
%t A199614 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199614 Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t A199614 r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
%t A199614 RealDigits[r]  (* A199613, least of 4 roots *)
%t A199614 r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t A199614 RealDigits[r]  (* A199614, greatest of 4 roots *)
%Y A199614 Cf. A199597.
%K A199614 nonn,cons
%O A199614 1,1
%A A199614 _Clark Kimberling_, Nov 08 2011